GATE Overflow Test Series | Spatial and Analytical Aptitude | Test 1 | Question: 2

Question

The diagram shows four identical white rectangles around a shaded square.

The area of the shaded square is __________$(\text{cm}^{2})$

Answer 1

The side length of shaded square is $ = 9-2 = 7\:\text{cm}.$

The are of square $ = a^{2},$ where $'a'$ is the side length of the square.

Now, the area of shaded square $ = 7^{2} = 49\:\text{cm}^{2}.$

So, the correct answer is $49.$

Answer 2

The area of square $ = a^{2},$ where $`a\text{’}$ is the side of the square.

The area of big square $ = 11^{2} = 121\;\text{cm}^{2}$

The area of rectangle $ = a b\;\text{cm}^{2},$ where $`a\text{’},$ and $`b\text{’}$ is the sides of the rectangle.

The area of rectangle $ = 2\cdot 9 = 18\;\text{cm}^{2}$

$\therefore$ The area of $4$ rectangles $ = 4 \times 18 = 72\;\text{cm}^{2}$

Thus, the area of shaded square $ = 121 – 72 = 49\;\text{cm}^{2}.$

So, the correct answer is $49.$