Rectangle

Q. Which of following properties are true for a rectangle?

1. All sides are equal.
2. All angles are equal.
3. Diagonals are equal in length.
4. Opposite sides are not parallel.

Q.

The length of a rectangle is 150 cm. If its breadth is 1 m, then its perimeter is _ cm

Q. The perimeter of a rectangle ABCD is 36 cm. If AB = CD and AD = BC and the measure of BC is twice the measure of AB. Find the measure of AB and BC.

1. AB = 6 cm and BC = 12 cm
2. AB = 12 cm and BC = 12 cm
3. AB = 12 cm and BC = 6 cm
4. AB = 4 cm and BC = 15 cm

Q. Given below is a Rectangle ABCD. Find the value of x and y.

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

Q. In a rectangle, if one diagonal is 20 cm, the other diagonal is ______.

1. 20 cm
2. 30 cm
3. 40 cm
4. 10 cm

Q.

Diagonals of a rectangle are equal and perpendicular. State whether the statement is true or false.

1. True

2. False

Q.
The measure of unknown angle x°, in the quadrilateral ABCD is .

1. 115°
2. 85°
3. 105°
4. 125°

Q. Given below is a rectangle ABCD. Find the value of x.

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

Q. Choose the correct statement(s) about rectangles and parallelograms.

1. Rectangles inherit all the properties of parallelograms
2. Rectangles inherit only some properties of parallelograms
3. All parallelograms need not be rectangles
4. All parallelograms are rectangles

Q.

If we know that one side of a rectangle is 8 cm. Can we construct a unique rectangle?

1. With measurement of one angle, yes

2. With measurement of two angle, yes

3. Yes, we can

4. No, its not possible

Q. Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm. [2 marks]

Q.

There was a kite making competition in Rahul’s school. Rahul and his group came up with a kite which looked like the one in the figure.

What is the area of the kite if the area of the red colored part is 50 ${\text{cm}}^2$?

1. 75 cm²

2. 50 cm²

3. 100 cm²

4. 120 cm²

Q. If the length and breadth of a rectangle are doubled, then its perimeter ____.

1. triples
2. doubles
3. becomes half
4. becomes 4 times

Q. If ABCD is a rectangle. If the diagonals are of the length (8x - 9) cm and (3x + 6) cm, then find the length of the diagonal.

1. 3 cm
2. 10 cm
3. 15 cm
4. 18 cm

Q. If the length and breadth of a rectangle are doubled, then its perimeter ____.

1. becomes 4 times
2. becomes half
3. doubles
4. triples

Q.

If we know that one side of a rectangle is 8 cm, we can construct a unique rectangle.

1. False

2. True

Q. Area of a rectangle of length(l) and breadth(b) units is given by 2$\times$(l+b) square units.

1. True
2. False

Q. The sum of the interior angles of a rectangle is _____.

1. ${360}^{\circ }$
2. ${180}^{\circ }$
3. ${90}^{\circ }$
4. ${135}^{\circ }$

Q. Mr. Graze, a farmer, has a rectangular field as shown. The longest possible length inside the field is the smallest prime number.
Find the ratio of the area of the field to the square of the perimeter of the field.

1. $\frac{\sqrt{6}}{4{\left(\sqrt{3}+1\right)}^2}$
2. $\frac{\sqrt{3}}{2{\left(\sqrt{3}+1\right)}^2}$
3. $\frac{\sqrt{3}}{4{\left(\sqrt{3}+1\right)}^2}$
4. $\frac{\sqrt{6}}{8{\left(\sqrt{3}+1\right)}^2}$

Q.

If the perimeter of a regular hexagon is $xmeters$, then the length of each of its sides is

1. $6+xmeters$

2. $6÷xmeters$

3. $x-6meters$

4. $x÷6meters$

Q.

A farmland shown in the figure below has a length of 15 m and breadth of 10 m. Pea is cultivated in the small area ABCD and in the remaining portion, paddy is cultivated. ABCD is a square with length 4 m. Find the area of the land where paddy is cultivated.

1. $134m^2$

2. $150m^2$

3. $16m^2$

4. $1500m^2$

Q. Answer the tick ones
1. Which of the following statements are true for a rectangle?
(i) It has two pairs of equal sides.
(ii)It has all its sides of equal length.
(iii) Its diagonal are equals.
(iv) Its diagonals bisect each other.
(v) Its diagonals are perpendicular.
(vi) Its diagonals are perpendicular and bisect each other.
(vii) Its diagonals are equal and bisect each other.
(viii)lts diagonals are equal and perpendicular, and bisect each other .
(ix) All rectangles are Squares.
(x) All rhombuses are parallelograms.
(xi)All squares are rhombuses and also rectangles.
(xii) All squares are not parallelograms.
2. Which of the following statements are true for a square?
(i) It is a rectangle.
(ii) It has all its sides of equal length.

Q. Quadrilateral ABCD is a rectangle such that the length of its diagonals AC, BD are $8x+8$ cm and $24x–8$ cm respectively. Find the value of $x$.

1. 1 cm
2. 2 cm
3. 3 cm
4. 4 cm

Q. The line joining the mid points of the diagonals of a trapezium has length $3$cm. If the longer base is $97$cm then the shorter base is:

1. $94$cm
2. $92$cm
3. $91$cm
4. $90$cm

Q. ${45}^{\circ }$ can be obtained by drawing the angles of measure

1. $10,30$
2. $15,30$
3. $60,90$

Q. Observe the following figure and find the measure of angle ∠AOD.

1. 150°
2. 140°
3. 120°
4. 100°

Q. In a hexagon ABCDEF, side AB is parallel to side FE and $\angle B:\angle C:\angle D:\angle E=6:4:2:3.$ Find $\angle B,\angle C,\angle D$ and $\angle E$.

1. $\angle B={216}^{\circ },\angle C={144}^{\circ },\angle D={72}^{\circ },\angle E={108}^{\circ }$
2. $\angle B={236}^{\circ },\angle C={144}^{\circ },\angle D={72}^{\circ },\angle E={120}^{\circ }$
3. $\angle B={226}^{\circ },\angle C={144}^{\circ },\angle D={72}^{\circ },\angle E={108}^{\circ }$
4. $\angle B={296}^{\circ },\angle C={180}^{\circ },\angle D={108}^{\circ },\angle E={144}^{\circ }$

Q. For the diagram above, the value of $x^{\circ }=$.

1. ${150}^{\circ }$
2. ${140}^{\circ }$
3. ${130}^{\circ }$

Q. Area of the triangle $MNO$ of Fig is

1. $\frac{1}{2}MN\times NO$
2. $\frac{1}{2}NO\times MO$
3. $\frac{1}{2}MN\times OQ$
4. $\frac{1}{2}NO\times OQ$

Q. ABC is a right angled at B with $BC=6$ and $AC=10cm$. Also $△ABC$ and $△BCD$ are on the same base $BC$. Find $ar\left(△BCD\right)$.

1. $12c{m}^2$
2. $24c{m}^2$
3. $6c{m}^2$
4. $48c{m}^2$