Question

This figure consists of a rectangle and a quarter circle.

What is the perimeter of this figure?

Use 3.14 for π.

Answer 1

Circumference=2 x 3.14 x radius
divide the circumference by 4 to get a quarter circle.

now add. 12.56+8+10+10+17+9=66.56

Answer 2

the perimeter of the figure is 66.56 cm.

Explanation:

Hello.

Let's remember the perimeter of a rectangle and the perimeter of a circle

`Perimeter\ of\ a\ rectangle=2(length)+2(width)\\Perimeter\ of\ a\ circle = 2\pi r \where\ r\ is\ the\ radius\ of\ the\ circle\\`

Now, the perimeter of a quarter circle is

`(Perimeter\ of\ a\ circle )/(4)=(2\pi r\ )/(4) \\\\Perimeter\ of\ a\ quarter\ circle=(\pi r)/(2)\\`

Step 1

find the perimeter of the rectangle

`Perimeter\ of\ a\ rectangle=2(length)+2(width)\\let\\length=17 cm\\width=10 cm\\\\Perimeter\ of\ the\ rectangle=2(17 cm )+2(10 cm)\\Perimeter\ of\ the\ rectangle= 34 cm +20 cm\\Perimeter\ of\ the\ rectangle=54 cm`

Step 2

find the perimeter of the quarter circle

`Perimeter\ of\ a\ quarter\ circle=(\pi r)/(2) \\let\ r =8 cm\\\\\pi =3.1\\Perimeter\ of\ the\ quarter\ circle=(3.14*8 cm)/(2) =12.56 cm\\Perimeter\ of\ the\ quarter\ circle=12.56 cm`

step 3

find the total perimeter

the right side of the quarter of circle has a vertical line ,r=8 cm, that must be added to the perimeter, and the rectangle has a line in common with the quarter of circle, r= 8cm=, this length must be subtracted from the total perimeter

the total perimeter is

find the perimeter of the rectangle+perimeter of the quarter circle +r-r

total perimeter=54 cm +12.56 cm+8 cm -8 cm

total perimeter= 66.56 cm

have a great day