4 Sides, 1 Angle

Q. Construction of quadrilaterals when four sides and one diagonal are given:
1. Construct a quadrilateral ABCD in which AB = 4.8 cm, BC = 4.3 cm, CD = 3.6 cm, AD = 4.2 cm and diagonal AC = 6 cm.

Q. Construction of quadrilaterals when three sides and two diagonals are given:
2. Construct a quadrilateral ABCD in which AB = 4 cm BC = 3.8 cm, AD = 3 cm, diagonal AC = 5 cm and diagonal BD = 4.6 cm.

Q.

Construct following quadrilaterals

(i) Quadrilateral $LIFT$
$LI=4cm$
$IF=3cm$
$TL=2.5cm$
$LF=4.5cm$
$IT=4cm$

Q.

Construct the following quadrilaterals.

(i) Quadrilateral $ABCD$

$AB=4.5cm$

$BC=5.5cm$

$CD=4cm$

$AD=6cm$

$AC=7cm$

Q. Construct a quadrilateral NICE with $NI=4.5cm,IC=4.3cm,NE=3.5cm,NC=5.5cm$ and $IE=5cm$. Also find its area.

Q. PQRS is a quadrilateral. Measure of PQ = 2.8 cm, QR = 3.1 cm, RS = 2.6 cm and SP = 3.3 cm and $\angle$SPQ = 60°. The steps of construction are as follows. What can be the missing step?

Step 1:
Draw a line segment PQ of length 2.8 cm.
Step 2 :
Construct an angle 60° at the point P and extend the line.
Step 3:
Draw an arc of 3.3 cm by taking P as the centre. Let the intersecting point be S.
Step 4: ?
Step 5:
Let the intersecting point of arcs be R. Connect R, to S and Q. PQRS is hence constructed.

1. Join SR. PQRS will be the required quadrilateral.
2. Draw an arc of 2.6 cm by taking S as the centre and another arc of 3.1 cm by taking Q as the centre.
3. Extend PQ to construct the point R
4. No steps are missed.

Q. The difference between the adjacent sides of rectangle is 1 cm. Construct the rectangle ABCD if the perimeter is 14 cm. Find the measure the length of the diagonals.

1. 8cm
2. 6cm
3. 5cm
4. 4cm

Q. Question 2
If the lengths of the diagonals of a rhombus are 16cm and 12cm. Then, the length of the sides of the rhombus is

(A) 9 cm
(B) 10 cm
(C) 8 cm
(D) 20 cm

Q. Construct Quadrilateral GOLD with OL=7.5 cm, GL= 6 cm, GD = 6 cm, LD = 5 cm, OD = 10 cm.

Q. For the construction of a parallelogram ABCD, the measurements of the length(s) , and $\angle A=65°$ is sufficient.

1. AC
2. AB
3. CD
4. AB and BC

Q. Find the area of quadrilateral whose diagonal length is $10$cm, height $h_1=5$cm and height $h_2$ is $7$cm.

Q. In a quadrilateral ABCD with AB = AD = 6cm, $\angle A=45°$ BC = 3.5cm, CD = 5cm , can we construct a point which is equidistant from BC and CD?

1. Yes.
2. Data insufficient.
3. Equidistant point cannot be found.
4. Never possible.

Q. Construct a quadrilateral ABCD with AB = 4 cm, BC = 6 cm, CD = 5.6 cm DA = 5 cm and AC = 8 cm. Find also its area.

Q. Construct a parallelogram, ABCD with side BC = 4.5 cm, diagonal AC = 5.6 cm and diagonal BD = 5.0 cm. [4 MARKS]

Q.

Construct a quadrilateral, ABCD has AB = 3.0 cm, BC = 4.0 cm, CD = 5.0 cm, DA = 3.5 cm and diagonal AC = 4.5 cm [2 MARKS]

Q. When a ball is thrown upwards, the time, $T$ seconds, during which the ball remains in the air is directly proportional to the square root of the height, $h$ metres, reached. We know $T=4.47sec$ when $h=25m$. Find the value of $T$ when $h=50$ give the answer correct to $3$ decimal places

Q.

Construct a quadrilateral ABCD in which AB = 2.7 cm, BC = 3.5 cm, CD = 4 cm, AD = 6 cm and $\angle B={90}^{\circ }$ [4 MARKS]

Q. To construct a parallelogram, BC = 4 cm , CD= 3 cm and ∠BCD = ${60}^{\circ }$
Determine all the other angles of the parallelogram.

1. ∠DAB= ${120}^{\circ }$ ∠ABC = ${60}^{\circ }$ and ∠ADC = ${120}^{\circ }$
2. ∠DAB= ${100}^{\circ }$ ∠ABC = ${100}^{\circ }$ and ∠ADC = ${100}^{\circ }$
3. ∠DAB= ${110}^{\circ }$ ∠ABC = ${50}^{\circ }$ and ∠ADC = ${130}^{\circ }$
4. ∠DAB= ${60}^{\circ }$ ∠ABC = ${120}^{\circ }$ and ∠ADC = ${120}^{\circ }$

Q. For the construction of a parallelogram ABCD, the measurements of the length(s) , and $\angle A=65°$ is sufficient.

1. AC
2. AB
3. CD
4. AB and BC

Q. Construct a quadrilateral ABCD such that AB=$3.5cm,$ BC=$4.5cm$, CD=$3.5cm,$
AD=$5.6cm$, AC=$6.6cm$.

Q.

Construct Quadrilateral GOLD with OL=7.5 cm, GL= 6 cm, GD = 6 cm, LD = 5 cm, OD = 10 cm. [3 MARKS]

Q. We can construct triangles when three angles are given.

1. False
2. True

Q. For the construction of a parallelogram ABCD, the measurements of the length(s) , and $\angle A=65°$ is sufficient.

1. AC
2. AB
3. CD
4. AB and BC

Q. Shubam was given a task of rearranging the steps for the construction of quadrilaterals. The data given was, PS = 4 cm, SR = 5 cm, RQ = 6 cm $\angle PSR$ = 100° and $\angle QRS$ = 120°. Find the correct order.
(a)
(b)(c)(d)

1. (c), (a), (b), (d)
2. (c), (d), (a), (b)
3. (d), (c), (a), (b)
4. (c), (d), (b), (a)

Q. We cannot construct a quadrilateral if the measurements of 4 angles and one side is given.

1. False
2. True

Q. Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, $\angle O={120}^{\circ },\angle R={105}^{\circ }$ and $\angle A={135}^{\circ }$? If not, why?

Q. For the construction of a parallelogram ABCD, the measurements of the length(s) , and $\angle A=65°$ is sufficient.

1. AB
2. AB and BC
3. CD
4. AC

Q. Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, $\angle O={120}^{\circ },\angle R={105}^{\circ }$ and $\angle A={135}^{\circ }$? If not, why?

Q. Constant a quadrilateral ABCD, when :
Angle A = ${90}^{\circ }$, AB = $4.6$ cm, BD = $6.4$ cm, AC = $6.0$ cm, and CD = $4.2$ cm.

Q. Construct a quadrilateral $ABCD$, when $AB=3cm,CD=3cm,DA=7.5cm,AC=8cm$ and $BD=4cm$.