Question

Find the perimeter and area of the given shape.

Accepted Answer

Given,

We have to find the perimeter and area of the given shape.

Area of the given shape $=$ Area of rectangle $+ (2 \times$ Area of semicircle $)$

Area of rectangle $= length \times breadth = 25 cm \times 7 cm = 175 {cm}^{2}$

Area of semicircle $= \frac{{πr}^{2}}{2} = (\frac{22}{7} \times 3.5 cm \times 3.5 cm \times \frac{1}{2}) = \frac{11 \times 12.25 {cm}^{2}}{7} = \frac{134.75 {cm}^{2}}{7} = 19.25 {cm}^{2}$

Area of the given shape $= 175 {cm}^{2} + (2 \times 19.25 {cm}^{2}) = 175 {cm}^{2} + 38.5 {cm}^{2} = 213.5 {cm}^{2}$

Perimeter of the given shape $=$ Perimeter of the rectangle $+ (2 \times$ Perimeter of semicircle $)$

Perimeter of the rectangle $= 2 (l + b) = 2 (25 cm + 7 cm) = 2 \times 32 cm = 64 cm$

Perimeter of semicircle $= R (π + 2) = 3.5 cm (\frac{22}{7} + 2) = 3.5 cm \times (\frac{22 + 14}{7}) = \frac{126}{7} = 18 cm$

Perimeter of the given shape $= 64 cm + 2 \times 18 cm = 64 cm + 36 cm = 100 cm$

Hence, the perimeter of the given shape is $100 cm$ and the area of the given shape is $213.5 {cm}^{2}$ .

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