Name: Perimeter of a Closed Semicircular Figure
Uploaded: 2019-07-19
Duration: 2 min 24 s
Description: We know how to calculate the circumference or perimeter of a circle. Let’s watch how to calculate the perimeter of a closed semicircular figure in this video.

Question

A square tile of length $20 cm$ has four quarter circles at each corner as shown in Fig. (i). Find the area of the shaded portion. Another tile with the same dimensions has a circle in the centre of the tile [Fig. (ii)]. If the circle touches all four sides of the square tile, find the area of the shaded portion. In which tile, area of the shaded portion will be more? $($ Take $π = 3.14)$

Accepted Answer

For figure (i):

Area of shaded portion $($ Area of square $π = 3.14)$ times of area of quarter circle

$= (20 \times 20) - (4 \times \frac{π r^{2}}{4})$
$= (400) - [4 \times (3.14 \times \frac{1}{4} \times 10^{2})]$
$= 400 - 314 = 86 {cm}^{2}$ .

For figure (ii):

Area of shaded portion $=$ Area of square -Area of circle $= (20 \times 20) - (π r^{2})$
$= 400 - (3.14 \times 10^{2})$
$= 400 - 314 = 86 {cm}^{2}$ .

Therefore, both cases have equal areas.

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