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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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