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.

18 cm

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12 cm

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15 cm

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9 cm

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Solution

The correct option is A
18 cm

Area of square = $S i d e^{2}$
$\Rightarrow$ 36 = $S i d e^{2}$
$\Rightarrow$ Side = 6 cm

Side of triangle = 6 cm

Semi perimeter of the triangle s $= \frac{6 + 6 + 6}{2} c m = 9 c m$

Area of the triangle $= \sqrt{s (s - a) (s - b) (s - c)}$
$= \sqrt{9 (9 - 6)^{3}}$
$= \sqrt{243}$
$= 9 \sqrt{3} c m$

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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.

The correct option is A 18 cm Area of square = Side2 ⇒ 36 = Side2 ⇒ Side = 6 cm Side of triangle = 6 cm Semi perimeter of the triangle s =6+6+62cm=9 cm Area of the triangle =√s(s−a)(s−b)(s−c) =√9(9−6)3 =√243 =9√3 cm

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.