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IrinaVladis [17]
3 years ago
15

Semicircles

Mathematics
1 answer:
Studentka2010 [4]3 years ago
8 0

Answer:

The area of the shaded portion of the figure is 9.1\ cm^2

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The shaded area is equal to the area of the square less the area not shaded.

There are 4 "not shaded" regions.

step 1

Find the area of square ABCD

The area of square is equal to

A=b^2

where

b is the length side of the square

we have

b=4\ cm

substitute

A=4^2=16\ cm^2

step 2

We can find the area of 2 "not shaded" regions by calculating the area of the square less two semi-circles (one circle):

The area of circle is equal to

A=\pi r^{2}

The diameter of the circle is equal to the length side of the square

so

r=\frac{b}{2}=\frac{4}{2}=2\ cm ---> radius is half the diameter

substitute

A=\pi (2)^{2}

A=4\pi\ cm^2

Therefore, the area of 2 "not-shaded" regions is:

A=(16-4\pi) \ cm^2

and the area of 4 "not-shaded" regions is:

A=2(16-4\pi)=(32-8\pi)\ cm^2

step 3

Find the area of the shaded region

Remember that the area of the shaded region is the area of the square less 4 "not shaded" regions:

so

A=16-(32-8\pi)=(8\pi-16)\ cm^2  

---> exact value

assume

\pi =3.14

substitute

A=(8(3.14)-16)=9.1\ cm^2

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