Question

Find the Area of the figure below, composed of a rectangle and a semicircle. Round to

Answer 1

Answer:

129.1 square units

Step-by-step explanation:

First, let's find the area of the rectangle. We can use the formula below.

$a=lw$

where $l$ is the length and $w$ is the width.

The length of the rectangle is 13 and the width is 8.

$l=13\\w=8$

Substitute the values into the formula.

$a=13*8$

$a=104$

Next, let's find the area of the semicircle. We can use the formula below.

$a=\frac{1}{2} *\pi r^2$

First, find the radius. The radius is half of the diameter, and the diameter is 8.

⇒ r= d/2

⇒ r= 8/2

⇒ r= 4

$a=\frac{1}{2} *\pi (4)^2$

Evaluate the exponent.

⇒ 4² = 4*4 = 16

$a=\frac{1}{2} *\pi *16$

Multiply pi and 16.

$a=\frac{1}{2} *50.2654825$

Multiply.

$a=25.1327412$

Finally, find the area of the figure.

Add the area of the rectangle (104) and the area of the semicircle (25.1327412)

$104+25.1327412$

$129.132741$

Round to the nearest tenth. The 3 in the hundredth place tells us to leave the 1 in the tenth place.

$129.1$

The area of the figure is about 129.1 (square units).