Question

In the square carpet below, find the area of the orange region.

• A. $2c{m}^2$
• B. $4c{m}^2$
• C. $6c{m}^2$
• D. $8c{m}^2$

Answer 1

The correct option is B

$4c{m}^2$

Now, we can clearly see that the area of the red part will be exactly equal to the orange part. Let us assume them as A.

Area of one yellow triangle $=(\frac{1}{2}\times 2\times 2)c{m}^2=2c{m}^2$

A (red part) + A (orange part) = Total square area - Area of 4 yellow triangles

$2\times A=(4\times 4)c{m}^2-(4\times 2)c{m}^2$

$2\times A=8c{m}^2$

So, area of orange part, $A=\left(\frac{8}{2}\right)c{m}^2=4c{m}^2$