Question

A square OPQR is inscribed in a quadrant OSQT. If OP = $5\sqrt{2}cm$, find the area (in $c{m}^2$) of the blue region. (Take $\pi$ = $3.14$)

• A. 35.25
• B. 25.25
• C. 28.5
• D. 25

Answer 1

The correct option is C 28.5

Given: side of the square OPQR = $5\sqrt{2}cm$
In order to find the area of the blue region, we need to find the area of the quadrant and subtract the area of the square from it.

In $△OPQ$, PQ = OP = $5\sqrt{2}cm$, since they are the sides of the square.
OQ can be found using Pyhtagorean theorem.
$O{Q}^2=O{P}^2+P{Q}^2$
$\Rightarrow O{Q}^2=(5\sqrt{2}{)}^2+(5\sqrt{2}{)}^2$
$\Rightarrow O{Q}^2=50+50=100$
$\therefore OQ=10cm$

Area of the quadrant = $\frac{\pi r^2}{4}$
= $\frac{\pi {10}^2}{4}$
= $25\pi$
= $25\times 3.14$
= 78.5 sq. cm.

Area of the square = $sid{e}^2$
= $(5\sqrt{2}{)}^2$
= 50 sq. cm.

Area of the region shaded in blue = Area of the quadrant - Area of the square
= 78.5 - 50
= 28.5 sq. cm.