Question

What is the area of the $△$ SOR? PQRS is a square.

• A. $2c{m}^2$
• B. $2\sqrt{2}c{m}^2$
• C. $1c{m}^2$
• D. $\frac{1}{2}c{m}^2$

Answer 1

The correct option is C

$1c{m}^2$

To find the Area of $△$ SOR which is right angled at O, we need to find the sides OS and OR.

OS = OR (Diagonals bisect each other at right angles in a square)

Side of the square = 2 cm

Diagonal PR = $\sqrt{P{S}^2+S{R}^2}$

= $\sqrt{2^2+2^2}$ = $2\sqrt{2}$ cm

OR = $\frac{2\sqrt{2}}{2}$ = $\sqrt{2}$ cm

$\Rightarrow$ OS = OR = $\sqrt{2}$ cm

$\therefore$ Area of $△$SOR = $\frac{1}{2}\times OS\times OR$

= $\frac{1}{2}\times \sqrt{2}\times \sqrt{2}$

= $1c{m}^2$