Question

Perimeter of the rhombus is 100 m and its diagonal is 40 m. find the area of rhombus.

Answer 1

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$\bf\:Perimeter\:of\:rhombus =4\times\:side$

$\bf\implies\:100= 4\times\:side$

$\bf\implies\:side=\dfrac{100}{4}$

$\bf\implies\:side= 25\:m$

We know that diagonals of a rhombus divides the rhombus in two equilateral triangle.

then,

Area of 1 equilateral triangle,

$\bf\:Semi\: perimeter=\dfrac{25+25+40}{2}$

$\bf\:semi\: perimeter=\dfrac{90}{2}$

$\bf\:semi\: perimeter=45\:m$

Now,

$\bf\boxed\star\green{\underline{\underline{{By\: Using\: Heron's\: Formula:-}}}}$

$\bf\:Area\:of\: triangle=\sqrt{s(s-a)(s-b)(s-c)}$

$\bf\:Area\:of\: triangle=\sqrt{45(45-40)(45-25)(45-25)}$

$\bf\:Area\:of\: triangle=\sqrt{45\times\:5\times\:20\times\:20}$

$\bf\:Area\:of\: triangle=300\:{m}^{2}$

then,

$\bf\:Area\:of\:rhombus=2\times\:300{m}^{2}$

$\bf\:Area\:of\:rhombus=600{m}^{2}$