Question

the figure shown is a rectangle with a semicircle on each end. what is the area of the figure? use 3.14 for x.z-dn.net/?f=%5Cpi" id="TexFormula1" title="\pi" alt="\pi" align="absmiddle" class="latex-formula"> 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

Answer:

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

Step-by-step explanation:

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

We find the area of the rectangle using the formula;

$Area = l\times w$

$\Rightarrow Area = 8\times 6$

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

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

The area of the semicircles

$=2\times \frac{1}{2}\times \pi \times r^2$

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

$=2\times \frac{1}{2}\times 3.14 \times 3^2$

$= 3.14 \times 9$

$=28.26\:in^2$

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

Answer 2

Answer:

A = 76.3 in^2

Step-by-step 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