Question

Match the given images with their respective areas of the shaded centre square.

• A. 20 sq.cm
• B. 24.2 sq.cm
• C. 7.2 sq.cm

Answer 1

Area of the centre square
= $\frac{1}{5}$ of the area of the larger square
The small triangles can be rearranged and we get 5 squares of equal size in each case, as shown in the figure below.

$\therefore$ The shaded centre square is $\frac{1}{5}$ of the original square.
Hence, its area is $\frac{1}{5}$ times the area of the larger square.
Case1:
Square of side = 11 cm
Area of a square = $side\times side$
$\therefore$ Area of this square = $11\times 11$ = 121 sq.cm
hence, area of the shaded centre square = $\frac{121}{5}$
= 24.2 sq.cm

Case2:
Square of side = 10 cm
Area of a square = $side\times side$
$\therefore$ Area of this square = $10\times 10$ = 100 sq.cm
hence, area of the shaded centre square = $\frac{100}{5}$
= 20 sq.cm

Case3:
Square of side = 6 cm
Area of a square = $side\times side$
$\therefore$ Area of this square = $6\times 6$ = 36 sq.cm
hence, area of the shaded centre square = $\frac{36}{5}$ = 7.2 sq.cm