Two semicircles are inscribed in a square with side 8 cm as shown. Find the area of the shaded region.

Area of square = 8 8 = 64 sq cm

Circle inscribed would touch all sides, meaning the diameter is equal to the side length. Thus the radius would be half the width, or 4 cm.

Area of circle = \(\pi r^{2}\)
= \(\pi 4^{2}\)
= 3.14 16
= 50.24 sq cm

Then remove the circle area from the square area.

64 - 50.24 = 9.76 sq cm.

This is if that is how the image looks.

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abidemiokin abidemiokin · Answer 2 · 2021-09-03T18:14:50-04:00

The area of the shaded region is 13.76 square centimeters.

Find the diagram relating to the question shown below:

Area of the shaded part = Area of the square - Are of the Two semicircles

Area of the square = L²

Given that

L = 8cm

Area of the square = 8² = 64cm²

r = 8/2 = 4cm

Area of semicircle = πr²/2

Area of the semicircle = 3.14(4)²/2

Area of one semicircle = 8 3.14

Area of one semicircle = 25.12cm²

Area of two semi-circles = 2 25.12

Area of two semi-circles = 50.24cm²

Area of the shaded region = Area of a square - Area of two semicircles

Area of the shaded region = 64 - 50.24

Area of the shaded region = 13.76cm²

Hence the area of the shaded region is 13.76 square centimeters.

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