- 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(h1+h2).
Given that,
d = 10 cm, h1 = 6 cm and h2 = 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(h1+h2).
Given that,
h1 = 6 cm and h2 = 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.
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