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

perimeter=28.85 cm

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)=(Area\ of\ the\ circle)/(2)\\A_(semicircle)=((\pi *(diameter)^(2) )/(4) )/(2)\\ \\A_(semicircle)={(\pi *(diameter)^(2) )/(8)`

so, the total area is

`A_(total)=A_(rectangle)+A_(semicircle)\\A_(total)=(base*heigth) + (\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) + (\pi *(diameter)^(2) )/(8)\\A_(total)=(5*8) + (3.14 *(5)^(2) )/(8)\\A_(total)=(40) + (3.14 *(25) )/(8)\\A_(total)=(40) + (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.