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

Area of the shaded region=

Question

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

hesgidiauE · Accepted Answer

the solution is written below

Vasquez · Accepted Answer

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 $π r^{2}$ 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.

$A_{1} = 12 \times 8$

$= 96 {unit}^{2}$

the area of 6 circles is calculated.

$A_{2} = 6 \times π r^{2}$

$= 6 \times 3.14 \times 2^{2}$

$= 75.36 {unit}^{2}$

The shaded region area is net difference between the areas.

$A_{1} - A_{2} = 96 - 75.36$

=20.64

$\approx 20.6 {unit}^{2}$

Therefore the blank is to be filled with 20.6

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