Height & Base of Parallelogram

Q.

Quadrilateral ABCD whose sides in metres are 9, 40, 28 and 15 respectively and the angle between the first two sides is a right angle. What is the area of quadilateral ABCD?

1. $310m^2$

2. $300m^2$

3. $306m^2$

4. $312m^2$

Q.

Two adjacent sides of a parallelogram are $15cm$ and $12cm$. If the distance between $15cm$ sides is $8cm$, then the distance between the $12cm$ sides is _____ $cm$.

1. 8

2. 6

3. 10

4. 12

Q. The length of two adjacent sides of a parallelogram are 5 cm and 3.5cm. One of its diagonals is 6.5cm long. Area of the parallelogram is

1. $13\sqrt{10}c{m}^2$
2. $23\sqrt{5}c{m}^2$
3. $10\sqrt{5}c{m}^2$
4. $10\sqrt{3}c{m}^2$

Q. Find the base of the parallelogram, if its area is 108 $c{m}^2$ and it height is 12 cm.

1. 10 cm
2. 9 cm
3. 12 cm
4. 6 cm

Q.

Let PQRS be a kite such that PQ > PS. Prove that ∠PQR > ∠PSR. (Hint: Join QS).

Q.

Find the area of a parallelogram $ABCD$ in which $AB=3cm,BC=7cm$ and $AC=8cm$.

1. 6 cm²

2. 12 cm²

3. 24 cm²

4. 18 cm²

Q. The given points plots the outline of the front-view of a house. If so, find the height of the topmost point of the house from its floor.

$\text{Points}$

$(2,3);(8,3);(8,7);(5,10);(2,7)$

1. 9 units
2. 10 units
3. 8 units
4. 7 units

Q.

Consider the following triangle,

Choose the correct one.

1. PQ + PR < RQ

2. PQ > QR

3. 2PQ < QR

4. 2PQ > QR

Q. The area of a rhombus one side of which measures 20 cm and one of whose diagonals is 24 cm, is -

1. $344c{m}^2$
2. $324c{m}^2$
3. $364c{m}^2$
4. $384c{m}^2$

Q. The point of concurrency of the altitudes of a triangle is known as

1. Incentre
2. Circle centre
3. Orthocentre
4. Centroid

Q. The length of two adjacent sides of a parallelogram are 5 cm and 3.5cm. One of its diagonals is 6.5cm long. Then, find the area of the parallelogram.

Q. A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is $100m$, then the altitude of the triangle is:

1. $100m$
2. $200m$
3. $100\sqrt{2}$ m
4. $10\sqrt{2}$ m

Q.

In the given figure, find the area of parallelogram ABCD, if the area of the shaded triangle is $9c{m}^2$

1. 42 square cm

2. 35 square cm

3. 20 square cm

4. 56 square cm

Q. The length of two adjacent sides of a parallelogram are 5 cm and 3.5cm. One of its diagonals is 6.5cm long. Then, find the area of the parallelogram.

Q. The adjacent sides of a parallelogram are $7.5cm$ and $4cm.$ If the distance between the longer vides is $2cm,$ find the distance between the shorter sides.

Q. A rectangular piece of land with an area of $240{\text{m}}^2$ is restructured to form a parallelogram of same area. If one of the sides of the parallelogram measures 15 m, then find the corresponding height.

1. 16 m
2. 15 m
3. 24 m
4. 10 m