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Question
A land is in the shape of rhombus. The perimeter of the land is 160 m and one of the diagonal is 48 m. Find the area of the land.
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Solution
Perimeter of the rhombus = 160 m
4 × side = 160
Side of a rhombus = `160/4`
= 40 m
In ΔABC, a = 40 m, b = 40 m, c = 48 m
s = `("a" + "b" + "c")/2`
= `(40 + 40 + 48)/2 "cm"`
= `128/2`
= 64 m
s – a = 64 – 40 = 24 m
s – b = 64 – 40 = 24 m
s – c = 64 – 48 = 16m
Area of the ΔABC = `sqrt(64 xx 24 xx 24 xx 16)`
= 8 × 24 × 4
= 768 sq.m
Since ABCD is a rhombus Area of two triangles are equal.
Area of the rhombus ABCD = (768 + 768) sq.m
= 1536 sq.m
∴ Area of the land = 1536 sq.m
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