Question

if area of an equilateral triangle is 100 root 3 cm then find the area of the square with its diagonal equal to side of the equilateral triangle​

Answer 1

Answer:

200 cm²

Step-by-step explanation:

area of eq. triangle

$\frac{ \sqrt{3} }{4} \times {a}^{2} = 100 \ \sqrt{3} \\ {a}^{2} = 100 \sqrt{3} \times \frac{4}{ \sqrt{3} } \\ {a}^{2} = 400 \\ a = \sqrt{400 } \\ a = 20 \: cm$

side of eq. triangle is equal to diagonal of square

so,

area of square = (1/2 ) x diagonal²

$\frac{1}{2} \times {20}^{2} \\ \frac{1}{2} \times 400 \\ 200 \: {cm}^{2}$

hope it helps