Question

Find the perimeter, in cm, of the composite figure. This image shows a rectangle and a semicircle. Use 3.14 for the value of pi.

Answer 1

Answer:

perimeter=28.85 cm

Step-by-step explanation:

Hello, I can help you with this

in this case, in this case it is posible divide the area into 2 more known shapes, a rectangle and a semicircle

let's remember

the area of a rectangle is given by

$A_{r}=base*heigth$

the area of a semicircle is given by

$A_{semicircle}=\frac{Area\ of\ the\ circle}{2}\\A_{semicircle}=\frac{\frac{\pi *(diameter)^{2} }{4} }{2}\\ \\A_{semicircle}={\frac{\pi *(diameter)^{2} }{8}$

so, the total area is

$A_{total}=A_{rectangle}+A_{semicircle}\\A_{total}=(base*heigth) + \frac{\pi *(diameter)^{2} }{8}$

Step one

Let

base=5 cm

heigth=8 cm

diameter of the circle=5 cm

Step 2

put the values into the equation

$A_{total}=(base*heigth) + \frac{\pi *(diameter)^{2} }{8}\\A_{total}=(5*8) + \frac{3.14 *(5)^{2} }{8}\\A_{total}=(40) + \frac{3.14 *(25) }{8}\\A_{total}=(40) + \frac{78.5 }{8}\\A_{total}=49.8125$

so, the total area is 49.81215 square centimeters

to find the perimeter you must add the sides of the rectangle

it is

perimeter of the rectangle =8+8+5=21 cm

now, the perimeter of the semicircle is =pi* radius

Perimeter=(3.14*diameter)/2

Perimeter=(3.14*5)/2

Perimeter=7.85

so, the total perimeter is =21 cm+7.85

total perimeter=28.85

Have a good day.