The area of a square is $36 c m^{2}$ . If the side of the square is equal to the side of an equilateral triangle, then find the area of the triangle.

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Solution

Area of a square $= {Side}^{2}$
$\Rightarrow 36 = {Side}^{2}$
$\Rightarrow Side = 6 c m$

Hence, side of triangle $= 6 c m$

Semi perimeter of the triangle, $s = \frac{6 + 6 + 6}{2} c m = 9 c m$
Area of the triangle $= \sqrt{s (s - a) (s - b) (s - c)}$
$= \sqrt{9 (9 - 6)^{3}}$
$= \sqrt{243}$
$= 9 \sqrt{3} c m^{2}$

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The area of a square is 36 cm2. If the side of the square is equal to the side of an equilateral triangle, then find the area of the triangle.

Area of a square =Side2 ⇒36=Side2 ⇒Side=6 cm Hence, side of triangle =6 cm Semi perimeter of the triangle, s=6+6+62 cm=9 cm Area of the triangle =√s(s−a)(s−b)(s−c) =√9(9−6)3 =√243 =9√3 cm2

The area of a square is $36 c m^{2}$ . If the side of the square is equal to the side of an equilateral triangle, then find the area of the triangle.