Question

What is the total area of the colored parts in the given figure?

• A. 144 sq in
• B. 36 sq in
• C. 81 sq in
• D. 72 sq in

Answer 1

The correct option is B 36 sq in

We can see that the outer square is divided into 4 equal parts.

Let's calculate the area of the colored portion for one part of the square.



Side of outer square = 6 in

∴ Area of outer square = Side × Side
= 6 in × 6 in
= 36 sq in

Sides of inner square = 3 in

∴ Area of inner square = Side × Side
= 3 in × 3 in
= 9 sq in

Now, if we look carefully at the figure given in the question, we can see that the white portion in an inner square has:

• 2 identical triangles
• A square

Dimensions of one triangle are:


Base = 6 in
Height = 3 in

Area of triangle $=\frac{1}{2}\times Base\times Height$

$=\frac{1}{2}\times 6\times 3$

= 9 sq in

Area of one triangle = 9 sq in

∴ Area of 2 triangles = 2 × 9 sq in
= 18 sq in

Now, the area of the colored region
= Area of outer square – Area of inner square – Area of two triangles
= 36 sq in – 9 sq in – 18 sq in
= 9 sq in

Hence, the area of the shaded portion for one part of the square is 9 sq in.

To calculate the total area of the colored regions, let's multiply 9 sq in by 4.

So, area of colored region = 9 sq in × 4
= 36 sq in