Example:
In a quadrilateral ABCD, diagonal AC = 10 cm. The lengths of perpendiculars from B and C to AC are 6 cm and 7 cm respectively. Find the area of the quadrilateral.

Solution: The area of a quadrilateral ABCD = 1/2 * d(h_{1}+h_{2}).
Given that,
d = 10 cm, h_{1} = 6 cm and h_{2} = 7 cm.
So required area = 1/2 * 10 (6+7)
= 1/2 * 10 * 13
= 5 * 13
= 65 sq.cm.

Example:
In a quadrilateral ABCD, the lengths of perpendiculars from B and C to AC are 6 cm and 4 cm respectively. Find the length of the diagonal if the area of the quadrilateral is given by 65 sq.cm.

Solution:
Let the length of the diagonal be 'x'. The area of a quadrilateral ABCD = 1/2 * d(h_{1}+h_{2}).
Given that,
h_{1} = 6 cm and h_{2} = 4 cm.
i.e 65 = 1/2 * x (6+4),
i.e 65 = 1/2 * x * 10,
i.e 65 x 2 = 10x,
i.e x = 130/10 = 13 cm.
Hence the length of the diagonal is 13 cm.

Directions: Read the above example carefully and answer the following questions:

In a quadrilateral ABCD, the lengths of perpendiculars from B and C to AC are 15.5 cm and 12.3 cm respectively. Find the length of the diagonal if the area of the quadrilateral is given by 472.6 sq.cm.