Conversion of One Quadrilateral to the Other with Same Area

Q.

The parallelogram PQRS is formed by joining together four equilateral triangles of side 1 unit, as shown in the figure.

What is the length of the diagonal SQ?

1. $\sqrt{7}units$

2. $\sqrt{8}units$

3. $\sqrt{6}units$

4. $\sqrt{5}units$

Q. ABCD is a parallelogram. P is the mid-point of AB. BD and CP intersect at Q such that CQ : QP = 3.1. If ar (ΔPBQ) = 10cm², find the area of parallelogram ABCD.

Q.

If two adjacent sides of a parallelogram are 11cm and 15 cm and one of its diagonals is 16 cm, then find the area of the parallelogram

Q.

Two adjacent side of a parallelogram are 74cm and 40cm and it's diagonal 102cm. Find its area.

Q. The area of triangle ABC is 15 cm sq. If ΔABC and a parallelogram ABPD are on the same base and between the same parallel lines then what is the area of parallelogram ABPD.

Q. If the below parallelogram is converted into a rectangle of the same area , the breadth of the rectangle would be ____.

1. 5 cm
2. 8 cm
3. 2.5 cm
4. 10 cm

Q.

If area of parallelogram ABCD is 25 cm² and on the same base CD, a triangle BCD is given such that area BCD = x cm², then value of x is

1. 20 cm²

2. 25 cm²

3. 15 cm²

4. 12.5 cm²

Q. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, find the height of the parallelogram.

Q.

Find the area of quadrilateral ABCD, if AB || CD and AB = CD is as shown in figure :

1. 40 cm²

2. 16 cm²

3. 25 cm²

4. 32 cm²

Q.

In the following figure, if ED = 10 cm, BG = 8 cm and BE = CD = 9 cm, then find the area of triangle CDF.

1. 80 cm²

2. 40 cm²

3. 50 cm²

4. 75 cm²

Q.

A triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Q. The parallelogram PQRS is formed by joining together four equilateral triangles of side 1 unit, as shown in the figure.

What is the length of the diagonal SQ?

Q. The parallelogram PQRS is formed by joining together four equilateral triangles of side 1 unit, as shown in the figure.
What is the length of the diagonal SQ?

1. $\sqrt{7}units$
2. $\sqrt{8}units$
3. $\sqrt{6}units$
4. $\sqrt{5}units$

Q. The parallelogram PQRS is formed by joining together four equilateral triangles of side 1 unit, as shown in the figure.
What is the length of the diagonal SQ?

1. $\sqrt{7}units$
2. $\sqrt{8}units$
3. $\sqrt{6}units$
4. $\sqrt{5}units$

Q. The parallelogram PQRS is formed by joining together four equilateral triangles of side 1 unit, as shown in the figure.
What is the length of the diagonal SQ?

1. $\sqrt{7}units$
2. $\sqrt{8}units$
3. $\sqrt{6}units$
4. $\sqrt{5}units$

Q. If ABCD is a trapezium, find the value of angle B.

1. 45 degree
2. 35 degree
3. 55 degree
4. 40 degree

Q. The parallelogram PQRS is formed by joining together four equilateral triangles of side 1 unit, as shown in the figure.
What is the length of the diagonal SQ?

1. $\sqrt{7}units$
2. $\sqrt{8}units$
3. $\sqrt{6}units$
4. $\sqrt{5}units$