Question

The area of an equilateral triangle describe on one side of a square is equal to half the area of the equilateral triangle describe on one of its diagonals

• A. True
• B. False

Answer 1

The correct option is A True

Let side of square be $a$, then its diagonal is $\sqrt{2}a$.

Area of equilateral triangle having side $a$ is $are{a}_1=\frac{\sqrt{3}{a}^2}{4}c{m}^2$

Area of equilateral triangle having side

$\sqrt{2}a$ is $are{a}_2=1/2\left(a/\sqrt{2}\right)\left(\sqrt{3/2}a\right)=\frac{\sqrt{3}(a\sqrt{2}{)}^2}{4}$ $=\frac{\sqrt{3}(a{)}^2}{2}$

Hence, $are{a}_1$ is half of $are{a}_2$.

So, the area of an equilateral triangle describe on one side of a square is equal to half the area of the equilateral triangle describe on one of its diagonals