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Let ABCD be a quadrilateral and AC, BD be diagonals. The length of BD = 20 cm and the heights of the triangles ABD and BCD are, respectively, 6 cm, 8
Question

Let ABCD be a quadrilateral and AC, BD be diagonals. The length of BD = 20 cm and the heights of the triangles ABD and BCD are, respectively, 6 cm, 8 cm. Find the area of the quadrilateral ABCD (in cm²).

A.

140

B.

120

C.

148

D.

1282

Correct option is A

Given:
BD = 20 cm
Height of triangle ABD = 6 cm
Height of triangle BCD = 8 cm
Formula Used:
Area of triangle = 12\frac 12​×Base×Height
Area of quadrilateral = Sum of areas of two triangles formed by one diagonal
Solution:
Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle BCD
Area of quadrilateral ABCD = 12×20×6+12×20×8\frac12×20×6+\frac12×20×8​​
Area of quadrilateral ABCD = 60 + 80 = 140 sq. cm.

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