Find the area of the shaded region. Round to the nearest tenth.

Khaleesi Herbert

Khaleesi Herbert

Answered question

2021-08-12

Find the area of the shaded region. Round to the nearest tenth.

Area of the shaded region=

Answer & Explanation

hesgidiauE

hesgidiauE

Skilled2021-08-13Added 106 answers

the solution is written below
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Vasquez

Vasquez

Expert2021-12-27Added 669 answers

Step 1

The are two shapes: rectangle and 6 circles

The area of rectangle is product of its unequal sides.

Area of circle is equal to πr2 where r is radius.

Now since the circles are tightly fit the sum of diameter of three circles (considered horizontally) is equal to 12.

3d=12

d=4

where d is diameter and d=2r

Therefore the radius of each equal circle is:

d=4

2r=4

r=2

Step 2

The area of rectangle is calculated.

A1=12×8

=96 unit2

the area of 6 circles is calculated.

A2=6×πr2

=6×3.14×22

=75.36 unit2

The shaded region area is net difference between the areas.

A1A2=9675.36

=20.64

20.6 unit2

Therefore the blank is to be filled with 20.6

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