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  • A field in the form of a parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. Find the area of the parallelogram.

A field in the form of a parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. Find the area of the parallelogram.

Answers (1)

[600\sqrt{15}m^{2} ]

We know that ABCD is parallelogram

So the opposite sides are equal.

AB = CD = 60 m, AD = BC = 40 m

Thus, Area\; of\; parallelogram = 2 \times Ar(\Delta ABC)

In \DeltaABC, using heron’s formula

Semi perimeter, S =\frac{60+40+80}{2}=\frac{180}{2}=90m

Area \; of\; \; triangle\; \Delta ABC =\sqrt{S\left ( S-a \right )\left ( S-b \right )\left ( S-c \right )}

=\sqrt{90\left ( 90-60 \right )\left ( 90-40 \right )\left ( 90-80 \right )}

=\sqrt{90\times 30\times 50\times 10}

=\sqrt{3\times 30\times 30\times 10\times 10\times 5}

= 30\times 10\sqrt{3\times 5}=300\sqrt{15}\; m^{2}

Hence,\; area\; of\; parallelogram =2\times 300\sqrt{15}\; m^{2}=600\sqrt{15}\; m^{2}

 

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infoexpert21

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