As the chapter is about Constructions, in Chapter 18 of RD Sharma Class 8 Maths, we shall learn how to construct a quadrilateral with given elements. Students are provided with exercise-wise solutions to help understand the concepts clearly from the exam point of view. The solutions are prepared by the experienced faculty team at BYJUâ€™S, who has explained the concepts in detail which is very helpful for preparing for their board exams. Students can download RD Sharma Class 8 PDF from the links given below.

Chapter 18- Practical Geometry (Constructions) contains five exercises and the RD Sharma Class 8 Solutions present in this page provide solutions to the questions present in each exercise. Now, let us have a look at the concepts discussed in this chapter.

- Construction of quadrilaterals.
- Constructing a quadrilateral when four sides and one diagonal are given.
- Constructing a quadrilateral when its three sides and the two diagonals are given.
- Constructing a quadrilateral when its four sides and one angle are given.
- Constructing a quadrilateral when its three sides and their included angles are given.
- Constructing a quadrilateral when its three angles and their two included sides are given.

## Download the Pdf of RD Sharma for Class 8 Maths Chapter 18 Practical Geometry (Constructions)

### Access answers to Maths RD Sharma Solutions For Class 8 Chapter 18 Practical Geometry (Constructions)

EXERCISE 18.1 PAGE NO: 18.4

**1. Construct a quadrilateralÂ ABCDÂ in whichÂ AB =Â 4.4 cm,Â BCÂ = 4 cm,Â CDÂ = 6.4 cm,Â DAÂ = 3.8 cm andÂ BDÂ = 6.6 cm.**

**Solution:**

The given details are AB =Â 4.4 cm,Â BCÂ = 4 cm,Â CDÂ = 6.4 cm,Â DAÂ = 3.8 cm andÂ BDÂ = 6.6 cm.

Divide the quadrilateral into two triangles i.e., Î”ABD and Î”BCD

Steps to construct a quadrilateral:

Step 1- By using SSS congruency rule, Draw line BD of length 6.6 cm.

Step 2- Cut an arc with B as the centre and radius BC = 4cm. Do the same by taking D as centre and radius CD = 6.4 cm.

Step 3- Now join the intersection point from B and D and label it as C.

Step 4- Now for vertex A, cut an arc by taking B as the center and radius BA = 4.4cm. Do the same by taking D as center and radius DA = 3.8cm.

Step 5- Join the intersection point from B and D and label it as A.

**2. Construct a quadrilateralÂ ABCDÂ in whichÂ AB = BCÂ = 5.5 cm,Â CDÂ = 4 cm,Â DAÂ = 6.3 cm,Â ACÂ = 9.4 cm MeasureÂ BD.**

**Solution:**

The given details are AB = BCÂ = 5.5 cm,Â CDÂ = 4 cm,Â DAÂ = 6.3 cm,Â ACÂ = 9.4 cm MeasureÂ BD.

Steps to construct a quadrilateral:

Step 1- Draw a line segment AB = 5.5cm

Step 2- With B as center and radius BC = 5.5cm cut an arc. Mark that point as C.

Step 3- With A as center and radius AC = 9.4cm cut an arc to intersect at point C.

Step 4- With C as center and radius CD = 4cm cut an arc. Mark that point as D.

Step 5- With A as center and radius AD = 6.3cm cut an arc to intersect at point D.

Step 6- Now join BC, CD and AD

Measure of BD is 5.1cm.

**3. Construct a quadrilateralÂ XYZWÂ in whichÂ XY =Â 5 cm,Â YZÂ = 6 cm,Â ZWÂ = 7 cm,Â WXÂ = 3 cm andÂ XZÂ = 9 cm.**

**Solution:**

The given details are XY =Â 5cm,Â YZÂ = 6cm,Â ZWÂ = 7cm,Â WXÂ = 3cm andÂ XZÂ = 9cm.

Steps to construct a quadrilateral:

Step 1- Draw line XZ of length 9cm.

Step 2- Cut an arc by taking X as the centre radius XY = 5cm. Do the same by taking Z as centre and radius ZY = 6cm.

Step 3- Now join the intersection point from X and Z and label it as Y.

Step 4- For vertex W, cut an arc by taking X as the center and radius XW = 3cm. Similarly, taking Z as the center and radius ZW = 7cm.

Step 5- Join the intersection point from X and Z and label it as W.

**4. Construct a parallelogramÂ PQRSÂ such thatÂ PQ =Â 5.2 cm,Â PRÂ = 6.8 cm, andÂ QSÂ = 8.2 cm.**

**Solution:**

The given details are PQ =Â 5.2 cm,Â PRÂ = 6.8 cm, andÂ QSÂ = 8.2 cm.

Steps to construct a parallelogram:

Step 1- Draw line QS of length 8.2 cm.

Step 2- Divide the line segment QS into half i.e 4.1 cm and mark that point as O. Now by taking O as center cut an arc on both the sides of O with a radius of 3.4cm each. And mark that points as P and R.

Step 3- cut an arc by taking Q as a center and radius QR = 5.2cm to intersect with point R.

Step 4- cut an arc by taking Q as a center and radius QP = 5.2cm to intersect with point P.

Step 5- Join sides PQ, PS, QR and RS.

**5. Construct a rhombus with side 6 cm and one diagonal 8 cm. Measure the other diagonal.**

**Solution:**

The given details are side 6 cm and one diagonal 8 cm.

We know all the sides of a rhombus are equal and diagonals bisect each other.

Steps to construct a rhombus:

Step 1- Draw a line XZ of length 8 cm.

Step 2- By taking a radius of 6 cm, cut an arc by taking X as the center. Do the same by taking Z as centre with radius of 6 cm.

Step 3- Now join the intersection point from X and Z and label it as Y.

Step 4- Now for vertex W, by taking radius of 6 cm and cut an arc by taking X as the center. Do the same by taking Z as center and radius of 6 cm.

Step 5- Join the intersection point from X and Z and label it as W.

Step 6- Now join XY, XW, XZ and ZY

**6. Construct a kiteÂ ABCDÂ in whichÂ AB =Â 4 cm,Â BCÂ = 4.9 cm,Â ACÂ = 7.2 cm.**

**Solution:**

The given details are AB =Â 4 cm,Â BCÂ = 4.9 cm,Â ACÂ = 7.2 cm.

Steps to construct a kite:

Step 1- Draw line AC of length 7.2 cm.

Step 2- By taking a radius of 4 cm and cut an arc by taking A as the center. Do the same by taking C as centre with radius of 4.9 cm.

Step 3- Now join the intersection point from A and C and label it as B.

Step 4- Now for vertex D, cut an arc by taking A as the center. Do the same by taking C as center with radius of 4.9 cm.

Step 5- Join the intersection point from A and C and label it as D.

**7. Construct, if possible, a quadrilateralÂ ABCDÂ givenÂ AB =Â 6 cm,Â BCÂ = 3.7 cm,Â CDÂ = 5.7 cm,Â ADÂ = 5.5 cm andÂ BDÂ = 6.1 cm. Give reasons for not being able to construct it, if you cannot.**

**Solution:**

The given details are AB =Â 6 cm,Â BCÂ = 3.7 cm,Â CDÂ = 5.7 cm,Â ADÂ = 5.5 cm andÂ BDÂ = 6.1 cm.

Steps to construct a quadrilateral:

Step 1- Draw a line AB of length 6cm.

Step 2- With A as a center cut an arc of radius 5.5cm and mark that point as D.

Step 3- With B as a center cut an arc of radius 6.1cm to intersect with point D.

Step 4- With B as a center cut an arc of radius 3.7cm and mark that point as C.

Step 5- With D as a center cut an arc of radius 5.7cm to intersect with point C.

Step 6- Now join AD, BD, BC and DC

**8. Construct, if possible, a quadrilateralÂ ABCDÂ in whichÂ AB =Â 6 cm,Â BCÂ = 7 cm,Â CDÂ = 3 cm,Â ADÂ = 5.5 cm andÂ ACÂ = 11 cm. Give reasons for not being able to construct, if you cannot. (Not possible, because in triangleÂ ACD,Â ADÂ +Â CD<AC).**

**Solution:**

The given details are AB =Â 6 cm,Â BCÂ = 7 cm,Â CDÂ = 3 cm,Â ADÂ = 5.5 cm andÂ ACÂ = 11 cm.

Such a Quadrilateral cannot be constructed because, in a triangle, the sum of the length of its two sides must be greater than that of the third side.

In triangle ACD,

AD + CD = 5.5 + 3 = 8.5 cm

Given, AC = 11 cm

So,Â AD + CD < AC which is not possible.

âˆ´ The construction is not possible

EXERCISE 18.2 PAGE NO: 18.6

**1. Construct a quadrilateralÂ ABCDÂ in whichÂ AB =Â 3.8 cm,Â BCÂ = 3.0 cm,Â ADÂ = 2.3 cm,Â ACÂ = 4.5 cm andÂ BDÂ = 3.8 cm.**

**Solution:**

The given details are AB =Â 3.8 cm,Â BCÂ = 3.0 cm,Â ADÂ = 2.3 cm,Â ACÂ = 4.5 cm andÂ BDÂ = 3.8 cm.

Steps to construct a quadrilateral:

Step 1- Draw a line AC = 6cm.

Step 2- Cut an arc of radius 3.8cm with A as the center to mark that point as B.

Step 3- Cut an arc of radius 3cm with C as the center to intersect with point B.

Step 4- Cut an arc of radius 3.8cm with B as the center to mark that point as D.

Step 5- Cut an arc of radius 2.3cm with A as the center to intersect with point D.

Step 6- Now join AB, BD, AD and DC

**2. Construct a quadrilateralÂ ABCDÂ in whichÂ BC =Â 7.5 cm,Â ACÂ =Â ADÂ = 6 cm,Â CDÂ = 5 cm andÂ BDÂ = 10 cm.**

**Solution:**

The given details are BC =Â 7.5 cm,Â ACÂ =Â ADÂ = 6 cm,Â CDÂ = 5 cm andÂ BDÂ = 10 cm.

Steps to construct a quadrilateral:

Step 1- Draw a line AC = 6cm.

Step 2- Cut an arc of radius 6cm with A as the center to mark that point as D.

Step 3- Cut an arc of radius 5cm with C as the center to intersect at point D.

Step 4- Cut an arc of radius 10cm with D as the center to mark that point as B.

Step 5- Cut an arc of radius 7.5cm with C as the center to intersect at point B.

Step 6- Now join AD, CD, DB and AB

**3. Construct a quadrilateralÂ ABCDÂ whenÂ AB =Â 3 cm,Â CDÂ = 3 cm,Â DAÂ = 7.5 cm,Â ACÂ = 8 cm andÂ BDÂ = 4 cm.**

**Solution:**

The given details are AB =Â 3 cm,Â CDÂ = 3 cm,Â DAÂ = 7.5 cm,Â ACÂ = 8 cm andÂ BDÂ = 4 cm.

Consider a triangle ABD from the given data,

So, AB + BD = 3+4 = 7cm

We know that sum of lengths of two sides of a triangle is always greater than the third side.

âˆ´ The construction is not possible.

**4. Construct a quadrilateralÂ ABCDÂ givenÂ AD =Â 3.5 cm,Â BCÂ = 2.5 cm,Â CDÂ = 4.1 cm,Â ACÂ = 7.3 cm andÂ BDÂ = 3.2 cm.**

**Solution:**

The given details are AD =Â 3.5 cm,Â BCÂ = 2.5 cm,Â CDÂ = 4.1 cm,Â ACÂ = 7.3 cm andÂ BDÂ = 3.2 cm.

Steps to construct a quadrilateral:

Step 1- Draw a line CD = 4.1cm

Step 2- Cut an arc of radius 7.3cm with C as the center to mark that point as A.

Step 3- Cut an arc of radius 3.5cm with D as the center to intersect at point A.

Step 4- Cut an arc of radius 3.2cm with D as the center to mark that point as B.

Step 5- Cut an arc of radius 2.5cm with C as the center to intersect at point B.

Step 6- Now join CA, DA, DB, CB and AB

**5. Construct a quadrilateralÂ ABCDÂ givenÂ AD =Â 5 cm, ABÂ = 5.5 cm,Â BCÂ = 2.5 cm,Â ACÂ = 7.1 cm andÂ BDÂ = 8 cm.**

**Solution:**

The given details are AD =Â 5 cm, ABÂ = 5.5 cm,Â BCÂ = 2.5 cm,Â ACÂ = 7.1 cm andÂ BDÂ = 8 cm.

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 5.5cm

Step 2- Cut an arc of radius 2.5cm with B as the center to mark that point as C.

Step 3- Cut an arc of radius 7.1cm with A as the center to intersect at point C.

Step 4- Cut an arc of radius 8cm with B as the center to mark that point as D.

Step 5- Cut an arc of radius 5cm with A as the center to intersect at point D.

Step 6- Now join BC, AC, BD, AD and CD

**6. Construct a quadrilateralÂ ABCDÂ in whichÂ BC =Â 4 cm,Â CAÂ = 5.6 cm,Â ADÂ = 4.5 cm,Â CDÂ = 5 cm andÂ BDÂ = 6.5 cm.**

**Solution:**

The given details are BC =Â 4 cm,Â CAÂ = 5.6 cm,Â ADÂ = 4.5 cm,Â CDÂ = 5 cm andÂ BDÂ = 6.5 cm.

Steps to construct a quadrilateral:

Step 1- Draw a line BC = 4cm

Step 2- Cut an arc of radius 6.5cm with B as the center to mark that point as D.

Step 3- Cut an arc of radius 5cm with C as the center to intersect at point D.

Step 4- Cut an arc of radius 5.6cm with C as the center to mark that point as A.

Step 5- Cut an arc of radius 4.5cm with D as the center to intersect at point A.

Step 6- Now join BD, CD, CA, DA and AB

EXERCISE 18.3 PAGE NO: 18.8

**1. Construct a quadrilateralÂ ABCDÂ in whichÂ AB =Â 3.8 cm,Â BCÂ = 3.4 cm,Â CDÂ = 4.5 cm,Â ADÂ = 5 cm andÂ âˆ BÂ = 80Â°.**

**Solution:**

The given details are AB =Â 3.8 cm,Â BCÂ = 3.4 cm,Â CDÂ = 4.5 cm,Â ADÂ = 5 cm andÂ âˆ BÂ = 80Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 3.8cm

Step 2- Construct and angle of 80^{o} at B.

Step 3- Cut an arc of radius 3.4cm with B as the center to mark that point as C.

Step 4- Cut an arc of radius 5cm with A as the center to mark that point as D.

Step 5- Cut an arc of radius 4.5cm with C as the center to intersect at point D.

Step 6- Now join BC, AD and CD

**2. Construct a quadrilateralÂ ABCDÂ given that AB =Â 8 cm,Â BCÂ = 8 cm,Â CDÂ = 10 cm,Â ADÂ = 10 cm andÂ âˆ AÂ = 45Â°.**

**Solution:**

The given details are AB =Â 8 cm,Â BCÂ = 8 cm,Â CDÂ = 10 cm,Â ADÂ = 10 cm andÂ âˆ AÂ = 45Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 8cm

Step 2- Construct and angle of 45^{o} at A.

Step 3- Cut an arc of radius 10cm with A as the center to mark that point as D.

Step 4- Cut an arc of radius 10cm with D as the center to mark that point as C.

Step 5- Cut an arc of radius 8cm with B as the center to intersect at point C.

Step 6- Now join AD, DC and BC

**3. Construct a quadrilateralÂ ABCDÂ in whichÂ AB =Â 7.7 cm,Â BCÂ = 6.8 cm,Â CDÂ = 5.1 cm,Â ASÂ = 3.6 cm andÂ âˆ CÂ = 120Â°.**

**Solution:**

The given details are AB =Â 7.7 cm,Â BCÂ = 6.8 cm,Â CDÂ = 5.1 cm,Â ASÂ = 3.6 cm andÂ âˆ CÂ = 120Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line DC = 5.1cm

Step 2- Construct and angle of 120^{o} at C.

Step 3- Cut an arc of radius 6.8cm with C as the center to mark that point as B.

Step 4- Cut an arc of radius 7.7cm with B as the center to mark that point as A.

Step 5- Cut an arc of radius 3.6cm with D as the center to intersect at point A.

Step 6- Now join CB, BA and DA

**4. Construct a quadrilateralÂ ABCDÂ in whichÂ AB = BCÂ = 3 cm,Â ADÂ =Â CDÂ = 5 cm andÂ âˆ BÂ = 120Â°.**

**Solution:**

The given details are AB = BCÂ = 3 cm,Â ADÂ =Â CDÂ = 5 cm andÂ âˆ BÂ = 120Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 3cm

Step 2- Construct and angle of 120^{o} at B.

Step 3- Cut an arc of radius 3cm with B as the center to mark that point as C.

Step 4- Cut an arc of radius 5cm with C as the center to mark that point as D.

Step 5- Cut an arc of radius 5cm with A as the center to intersect at point D.

Step 6- Now join BC, CD and DA

**5. Construct a quadrilateralÂ ABCDÂ in whichÂ AB =Â 2.8 cm,Â BCÂ = 3.1 cm,Â CDÂ = 2.6 cm andÂ DAÂ = 3.3 cm andÂ âˆ AÂ = 60Â°.**

**Solution:**

The given details are AB =Â 2.8 cm,Â BCÂ = 3.1 cm,Â CDÂ = 2.6 cm andÂ DAÂ = 3.3 cm andÂ âˆ AÂ = 60Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 2.8cm

Step 2- Construct and angle of 60^{o} at A.

Step 3- Cut an arc of radius 3.3cm with A as the center to mark that point as D.

Step 4- Cut an arc of radius 2.6cm with D as the center to mark that point as C.

Step 5- Cut an arc of radius 3.1cm with B as the center to intersect at point C.

Step 6- Now join AD, DC and CB

**6. Construct a quadrilateralÂ ABCDÂ in whichÂ AB = BCÂ = 6 cm,Â AD = DCÂ = 4.5 cm andÂ âˆ BÂ = 120Â°.**

**Solution:**

The given details are AB = BCÂ = 6 cm,Â AD = DCÂ = 4.5 cm andÂ âˆ BÂ = 120Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 6cm

Step 2- Construct and angle of 120^{o} at B.

Step 3- Cut an arc of radius 6cm with B as the center to mark that point as C.

Here, AC is about 10.3cm in length which is greater than AD + CD = 4.5+4.5=9cm

We know that sum of the two sides of a triangle is always greater than the third side.

AD + CD < AC

âˆ´ Construction is not possible.

EXERCISE 18.4 PAGE NO: 18.10

**1. Construct a quadrilateralÂ ABCDÂ in whichÂ AB =Â 6 cm,Â BCÂ = 4 cm,Â CDÂ = 4 cm,Â âˆ BÂ = 95Â° andÂ âˆ CÂ = 150Â°.**

**Solution:**

The given details are AB =Â 6 cm,Â BCÂ = 4 cm,Â CDÂ = 4 cm,Â âˆ BÂ = 95Â° andÂ âˆ CÂ = 150Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line BC = 4cm

Step 2- Construct and angle of 95^{o} at B.

Step 3- Cut an arc of radius 6cm with B as the center to mark that point as A.

Step 4- Construct and angle of 90^{o} at C.

Step 5- Cut an arc of radius 4cm with C as the center to mark that point as D.

Step 6- Now join BA, CD and AD

**2. Construct a quadrilateralÂ ABCDÂ whereÂ AB =Â 4.2cm,Â BCÂ = 3.6 cm,Â CDÂ = 4.8 cm,Â âˆ BÂ = 30Â° andÂ âˆ CÂ = 150Â°.**

**Solution:**

The given details are AB =Â 4.2cm,Â BCÂ = 3.6 cm,Â CDÂ = 4.8 cm,Â âˆ BÂ = 30Â° andÂ âˆ CÂ = 150Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line BC = 3.6cm

Step 2- Construct and angle of 30^{o} at B.

Step 3- Cut an arc of radius 4.2cm with B as the center to mark that point as A.

Step 4- Construct and angle of 150^{o} at C.

Step 5- Cut an arc of radius 4.8cm with C as the center to mark that point as D.

Step 6- Now join BA, CD and AD

**3. Construct a quadrilateralÂ PQRSÂ in whichÂ PQ =Â 3.5 cm,Â QRÂ = 2.5 cm,Â RSÂ = 4.1 cm,Â âˆ QÂ = 75Â° andÂ âˆ RÂ = 120Â°.**

**Solution:**

The given details are PQ =Â 3.5 cm,Â QRÂ = 2.5 cm,Â RSÂ = 4.1 cm,Â âˆ QÂ = 75Â° andÂ âˆ RÂ = 120Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line QR = 2.5cm

Step 2- Construct and angle of 75^{o} at Q.

Step 3- Cut an arc of radius 3.5cm with Q as the center to mark that point as P.

Step 4- Construct and angle of 120^{o} at R.

Step 5- Cut an arc of radius 4.1cm with R as the center to mark that point as S.

Step 6- Now join QP, RS and PS

**4. Construct a quadrilateralÂ ABCDÂ givenÂ BCÂ = 6.6 cm,Â CDÂ = 4.4 cm,Â ADÂ = 5.6 cmÂ âˆ DÂ = 100Â° andÂ âˆ CÂ = 95**

**Solution:**

The given details are BCÂ = 6.6 cm,Â CDÂ = 4.4 cm,Â ADÂ = 5.6 cmÂ âˆ DÂ = 100Â° andÂ âˆ CÂ = 95

Steps to construct a quadrilateral:

Step 1- Draw a line DC = 4.4cm

Step 2- Construct and angle of 100^{o} at D.

Step 3- Cut an arc of radius 5.6cm with D as the center to mark that point as A.

Step 4- Construct and angle of 90^{o} at C.

Step 5- Cut an arc of radius 6.6cm with C as the center to mark that point as B.

Step 6- Now join DA, CB and AB

**5. Construct a quadrilateralÂ ABCDÂ in whichÂ AD =Â 3.5 cm,Â ABÂ = 4.4 cm,Â BCÂ = 4.7 cm,Â âˆ AÂ = 125Â° andÂ âˆ BÂ = 120Â°.**

**Solution:**

The given details are AD =Â 3.5 cm,Â ABÂ = 4.4 cm,Â BCÂ = 4.7 cm,Â âˆ AÂ = 125Â° andÂ âˆ BÂ = 120Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 4.4cm

Step 2- Construct and angle of 125^{o} at A.

Step 3- Cut an arc of radius 3.5cm with A as the center to mark that point as D.

Step 4- Construct and angle of 120^{o} at B.

Step 5- Cut an arc of radius 4.7cm with B as the center to mark that point as C.

Step 6- Now join AD, BC and CD

**6. Construct a quadrilateralÂ PQRSÂ in whichÂ âˆ QÂ = 45Â° andÂ âˆ RÂ = 90Â°,Â QR =Â 5 cm,Â PQÂ = 9 cm andÂ RSÂ = 7 cm.**

**Solution:**

The given details are âˆ QÂ = 45Â° andÂ âˆ RÂ = 90Â°,Â QR =Â 5 cm,Â PQÂ = 9 cm andÂ RSÂ = 7 cm.

Steps to construct a quadrilateral:

Step 1- Draw a line QR = 5cm

Step 2- Construct and angle of 45^{o} at Q.

Step 3- Cut an arc of radius 9cm with Q as the center to mark that point as P.

Step 4- Construct and angle of 90^{o} at R.

Step 5- Cut an arc of radius 7cm with R as the center to mark that point as S.

Step 6- Now join QP, RS

Since the line segment QP and RS are not intersecting at each other, quadrilateral cannot be formed.

**7. Construct a quadrilateralÂ ABCDÂ in whichÂ AB = BCÂ = 3 cm,Â ADÂ = 5 cm,Â âˆ AÂ = 90Â° andÂ âˆ BÂ = 105Â°.**

**Solution:**

The given details are AB = BCÂ = 3 cm,Â ADÂ = 5 cm,Â âˆ AÂ = 90Â° andÂ âˆ BÂ = 105Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 3cm

Step 2- Construct and angle of 90^{o} at A.

Step 3- Cut an arc of radius 5cm with A as the center to mark that point as D.

Step 4- Construct and angle of 105^{o} at B.

Step 5- Cut an arc of radius 3cm with B as the center to mark that point as C.

Step 6- Now join AD, BC and CD

**8. Construct a quadrilateralÂ BDEF,Â whereÂ DE =Â 4.5 cm,Â EFÂ = 3.5 cm,Â FBÂ = 6.5 cm,Â âˆ FÂ = 50Â° andÂ âˆ EÂ = 100Â°.**

**Solution:**

The given details are DE =Â 4.5 cm,Â EFÂ = 3.5 cm,Â FBÂ = 6.5 cm,Â âˆ FÂ = 50Â° andÂ âˆ EÂ = 100Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line EF = 3.5cm

Step 2- Construct and angle of 100^{o} at E.

Step 3- Cut an arc of radius 4.5cm with E as the center to mark that point as D.

Step 4- Construct and angle of 50^{o} at F.

Step 5- Cut an arc of radius 6.5cm with F as the center to mark that point as B.

Step 6- Now join DE, FB and DB

EXERCISE 18.5 PAGE NO: 18.13

**1. Construct a quadrilateralÂ ABCDÂ given thatÂ AB =Â 4 cm,Â BCÂ = 3 cm,Â âˆ AÂ = 75Â°,Â âˆ BÂ = 80Â° andÂ âˆ CÂ = 120Â°.**

**Solution:**

The given details are AB =Â 4 cm,Â BCÂ = 3 cm,Â âˆ AÂ = 75Â°,Â âˆ BÂ = 80Â° andÂ âˆ CÂ = 120Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 4cm

Step 2- Construct and angle of 75^{o} at A.

Step 3- Construct and angle of 80^{o} at B.

Step 4- Cut an arc of radius 3cm with B as the center to mark that point as C.

Step 5- Construct and angle of 120^{o} at C such that it meets the line segment AX, mark that point as D.

Step 6- Now join BC, CD and DA

**2. Construct a quadrilateralÂ ABCDÂ whereÂ AB =Â 5.5 cm,Â BCÂ = 3.7 cm,Â âˆ AÂ = 60Â°,Â âˆ BÂ = 105Â° andÂ âˆ DÂ = 90Â°.**

**Solution:**

The given details are AB =Â 5.5 cm,Â BCÂ = 3.7 cm,Â âˆ AÂ = 60Â°,Â âˆ BÂ = 105Â° andÂ âˆ DÂ = 90Â°.

We know that âˆ AÂ + âˆ BÂ + âˆ CÂ + âˆ DÂ = 360^{o}

âˆ´ âˆ CÂ = 105^{o}

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 5.5cm

Step 2- Construct and angle of 60^{o} at A.

Step 3- Construct and angle of 105^{o} at B.

Step 4- Cut an arc of radius 3.7cm with B as the center to mark that point as C.

Step 5- Construct and angle of 105^{o} at C such that it meets the line segment AX, mark that point as D.

Step 6- Now join BC, CD and DA

**3. Construct a quadrilateralÂ PQRSÂ whereÂ PQ =Â 3.5 cm,Â QRÂ = 6.5 cm,Â âˆ PÂ =Â âˆ RÂ = 105Â° andÂ âˆ SÂ = 75Â°.**

**Solution:**

The given details are PQ =Â 3.5 cm,Â QRÂ = 6.5 cm,Â âˆ PÂ =Â âˆ RÂ = 105Â° andÂ âˆ SÂ = 75Â°.

We know that âˆ PÂ + âˆ QÂ + âˆ RÂ + âˆ SÂ = 360^{o}

âˆ´ âˆ QÂ = 75^{o}

Steps to construct a quadrilateral:

Step 1- Draw a line PQ = 3.5cm

Step 2- Construct and angle of 105^{o} at P.

Step 3- Construct and angle of 75^{o} at Q.

Step 4- Cut an arc of radius 6.5cm with Q as the center to mark that point as R.

Step 5- Construct and angle of 105^{o} at R such that it meets the line segment PX, mark that point as S.

Step 6- Now join QR, RS and PS

**4. Construct a quadrilateralÂ ABCDÂ whenÂ BCÂ = 5.5 cm,Â CDÂ = 4.1 cm,Â âˆ AÂ = 70Â°,Â âˆ BÂ = 110Â° andÂ âˆ DÂ = 85Â°.**

**Solution:**

The given details are BCÂ = 5.5 cm,Â CDÂ = 4.1 cm,Â âˆ AÂ = 70Â°,Â âˆ BÂ = 110Â° andÂ âˆ DÂ = 85Â°.

We know that âˆ AÂ + âˆ BÂ + âˆ CÂ + âˆ DÂ = 360^{o}

âˆ´ âˆ CÂ = 95^{o}

Steps to construct a quadrilateral:

Step 1- Draw a line BC = 5.5cm

Step 2- Construct and angle of 110^{o} at B.

Step 3- Construct and angle of 95^{o} at C.

Step 4- Cut an arc of radius 4.1cm with C as the center to mark that point as D.

Step 5- Construct and angle of 85^{o} at D such that it meets the line segment BX, mark that point as A.

Step 6- Now join CD, DA and BA

**5. Construct a quadrilateralÂ ABCDÂ âˆ AÂ = 65Â°,Â âˆ BÂ = 105Â°,Â âˆ CÂ = 75Â°,Â BCÂ = 5.7 cm andÂ CDÂ = 6.8 cm.**

**Solution:**

The given details are âˆ AÂ = 65Â°,Â âˆ BÂ = 105Â°,Â âˆ CÂ = 75Â°,Â BCÂ = 5.7 cm andÂ CDÂ = 6.8 cm.

We know that âˆ AÂ + âˆ BÂ + âˆ CÂ + âˆ DÂ = 360^{o}

âˆ´ âˆ DÂ = 115^{o}

Steps to construct a quadrilateral:

Step 1- Draw a line BC = 5.7cm

Step 2- Construct and angle of 105^{o} at B.

Step 3- Construct and angle of 105^{o} at C.

Step 4- Cut an arc of radius 6.8cm with C as the center to mark that point as D.

Step 5- Construct and angle of 115^{o} at D such that it meets the line segment BX, mark that point as A.

Step 6- Now join CD, DA and BA

**6. Construct a quadrilateralÂ PQRSÂ in whichÂ PQ =Â 4 cm,Â QRÂ = 5 cmÂ âˆ PÂ = 50Â°,Â âˆ QÂ = 110Â° andÂ âˆ RÂ = 70Â°.**

**Solution:**

The given details are PQ =Â 4 cm,Â QRÂ = 5 cmÂ âˆ PÂ = 50Â°,Â âˆ QÂ = 110Â° andÂ âˆ RÂ = 70Â°.

Steps to construct a quadrilateral:

Step 1- Draw a line PQ = 4cm

Step 2- Construct and angle of 50^{o} at P.

Step 3- Construct and angle of 110^{o} at Q.

Step 4- Cut an arc of radius 5cm with Q as the center to mark that point as R.

Step 5- Construct and angle of 70^{o} at R such that it meets the line segment PX, mark that point as S.

Step 6- Now join QR, RS and PS