The diagonals of a quadrilateral are perpendicular to each other and their lengths are 16 centimetres and 10 centimetres. What is its area?

Open in App

Solution

Let the given quadrilateral be ABCD with AC = 10 cm, BD = 16 cm.

Given: AC and BD are perpendicular to each other.

Area of ΔABD =

Area of ΔBCD =

Now, area of the quadrilateral ABCD = Area of ΔABD + Area of ΔBCD

= (8 cm × AE) + (8 cm × CE)

= 8 cm × (AE + CE)

= 8 cm × AC

= 8 cm × 10 cm

= 80 cm²

Suggest Corrections

Similar questions

One diagonal of a quadrilateral is 35 centimetres long and the perpendiculars to it from the opposite vertices are 15 centimetres and 19 centimetres long. What is the area of this quadrilateral?

The diagonals of a rhombus are of lengths 16 centimetres and 12 centimetres. What is its perimeter?

A B C D

is a parallelogram whose diagonals intersects each other at right angles if the length of the diagonals are

16

centimetre and

12

centimetre find the length of all sides and its perimeter

The area of a quadrilateral is 1470 square centimeters and the length of one of its diagonals is 42 centimetres. Calculate the sum of the lengths of the perpendiculars to this diagonal from the opposite vertices.

Two sides of a parallelogram are of length 6 centimetres and 4 centimetres and the angle between them is 35°. What are the lengths of its diagonals?

Join BYJU'S Learning Program