A rectangle is placed around a semicircle as shown below. The width of the rectangle is 4mm . Find the area of the shaded region

Question

Katena32 [7]

3 years ago

8

A rectangle is placed around a semicircle as shown below. The width of the rectangle is 4mm . Find the area of the shaded region

.

Mathematics

1 answer:

cestrela7 [59] · Answer 1 · 2022-07-27T02:58:57+03:00

Formulas:
Area_semicircle = Πr2/2
Area_rectangle = lw

Given:
Semicircle is engraved in the rectangle
length_rectangle = 8

Assumption:
Diameter of semicircle is equivalent to length of rectangle
diameter_semicircle = length_rectangle
diameter_semicircle = 8

Based on assumption, radius_semicircle is equal to the width of the rectangle.
diameter_semicircle/2 = radius_semicircle
radius_semicircle = 4 = width of rectangle

Solve:
Area_rectangle = l*w = 4*8 = 32
Area_semicircle = Πr2/2 = Π(4)2/2 = 8Π = 25.12

<span> Area_rectangle - Area_semicircle = 32 - 25.12 = 6.88</span>