Question

the figure shown is a rectangle with a semicircle on each end. what is the area of the figure? use 3.14 for
`\pi` and round your answer to the nearest tenth. a. 76.3
`x^(2)`, b. 104.5 in^2, c. 34.8 in^2, or d. 161.0 in^2? PLEASE HELP!

Answer 1

A = 76.3 in^2

Explanation:

We have a rectangle with a semicircle on each end.

We can find the area by adding the areas of each figure

The area of the rectangle is

A = l*w

The length is 8 and the width is 6

A = 8*6 = 48

If we have 2 semicircles ( 2 1/2 circles, we have 1 circle since the diameters are the same)

The area of a circle is

A = pi r^2

The diameter is 6 so the radius is 1/2 of the diameter

r = 1/2 (6) =3

A = pi * (3)^2

A = (3.14) * 9

A = 28.26

The area of the total figure is the area of the rectangle plus the area of the two semicircles ( or 1 circle since the diameters of the semicircle is the same)

A = 48+28.26

A =76.26

To the nearest tenth

A = 76.3 in^2

Answer 2

`\boxed{a.\:\:\:76.3\:in^2}`

Explanation:

The figure is made up of a rectangle and two semicircles.

We find the area of the rectangle using the formula;

`Area = l* w`

`\Rightarrow Area = 8* 6`

`\Rightarrow Area = 48\:in^2.`

We find the area of one of the semicircles and multiply by 2;

The area of the semicircles

`=2* (1)/(2)* \pi * r^2`

We substitute
`\pi =3.14` and
`r=3\:in` to obtain;

`=2* (1)/(2)* 3.14 * 3^2`

`= 3.14 * 9`

`=28.26\:in^2`

The area of the figure is

`=48+28.26`

`=76.26\:in^2`

To the nearest tenth we have;

`=76.3\:in^2`

The correct answer is A