Mathematics: Semicircleswhose centers aare the midpoints .of the sides ofsquare abcd are .drawn. if themeasure of eachside of the squareis 4 cm, what is the area, nearest tothe tenth of a sq cm, of the shadedportion of the figure?

Semicircleswhose centers aare the midpoints .of

Ответ:

memeE15

14.01.2022

Mathematics

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

$r=\frac{b}{2}=\frac{4}{2}=2\ cm$ ---> 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:

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

---> exact value

assume

$\pi =3.14$

substitute

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

Semicircleswhose centers aare the midpoints .of the sides ofsquare abcd are .drawn. if themeasure of

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Semicircles
whose centers a
are the midpoints .
of the sides of
square abcd are .
drawn. if the
measure of each
side of the square
is 4 cm, what is the area, nearest to
the tenth of a sq cm, of the shaded
portion of the figure?

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