Question

In the adjoining figure, semi-circles have been drawn on each side of a
square. Find the perimeter and area of the figure.​

Answer 1

Answer:

Perimeter = 36 cm

Area = 32 cm

Explanation:

PERIMETER

SQUARE

Given,

side of square= 3.5 cm

Perimeter of square = 4 * side

= 4* 3.5

= 14 cm

SEMI CIRCLE

Given,

side of square = diameter of semi circle = 3.5 cm

Therefore,

radius, r = 3.5 / 2 = 1.75 cm

Perimeter of semi circle = r ( π + 2)

= 1.75 ( 3.14 + 2 )

= 1.75 * 5.14

= 8.995 or 9 cm

Since there are four semicircles in the figure,

Total perimeter of the figure = 4 * perimeter of one semicircle

= 4 * 9

= 36 cm

AREA

SQUARE

Area of square = side²

= 3.5 * 3.5

= 12.25 cm

SEMI CIRCLE

Area of semi circle = 1/2 (πr²)

= 1/2 (3.14 * 1.75 * 1.75)

= 1/2 * 9.62

= 4.81 cm

Area of figure = area of square + 4 * area of semicircle

= 12.25 + 4 * 4.81

= 12.25 + 19.24

= 31.49 or 32 cm

Note : My decimal values can be wrong but I think the method is correct.

Hope it helps..❤️