The sides of a quadrilateral ABCD are AB $= 13 c m, B C = 16 c m, C D = 20 c m$ and $D A = 5 c m$ . If $B D = 12 c m$ ,find the area of the quadrilateral, using Heron's formula.

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Solution

Consider ΔABD :
s = (13 + 5 + 12)/2 cm
s = 15 cm
By heron formula, Area of ΔABC
$= \sqrt{15 \times (15 - 13) \times (15 - 5) \times (15 - 12)}$ cm²
= 30 cm²
Consider ΔBCD :
s = (16 + 20 + 12)/2 cm
s = 24 cm
By heron formula, Area of ΔBCD
$= \sqrt{24 \times (24 - 16) \times (24 - 20) \times (24 - 12)}$ cm²
= 96 cm²
Area of quadrilateral ABCD
= Area of ΔABC + Area of ΔBCD
= (30 + 96) cm²
= 126 cm²

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