Question

What is the perimeter and area of the semicircle with a diameter of 14 m?

Answer 1

The circumference (perimeter) of the semicircle = `35.99 m`
The area of the semicircle = `76.96 m^2`

Explanation:

In circles, perimeter and area are both related to diameter, so if you are given the diameter, you can figure out the perimeter and area.

The problem wants the area of a `"semicircle"`, so it's best to figure out the area of a complete circle first, and then divide it in half for the area of the semicircle.

Figuring out the perimeter is a little more complicated.

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Use the diameter to find the area of the semicircle

The formula for the area of a circle is
`A = pi  r^2`

Because the diameter is 14 meters, then the radius must be 7 meters.

So sub in `7` for `r` and solve for Area

`A_o= pi  r^2`
`A_o = pi  (7)^2`

`A_o = 49  pi`  square  meters `larr` exact answer
`A_o = 153.93` square meters `larr`rounded to the nearest hundredth

The area of the complete circle is `153.93  m^2`

So the area of the semicircle is half of that
`A_"semicircle"` `= 76.96  m^2` `larr` answer for the area of the semicircle

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Use the diameter to find the perimeter of the semicircle

To start, find the perimeter of the entire circle

`P = pi    d`
`P = pi (14)`

`Perimeter_o = 14 pi` `larr` exact answer
`Perimeter_o = 43.98` `larr` answer to the nearest hundredth

The perimeter of the semicircle is not as simple as "half the perimeter of the entire circle."

That is because the semicircle also has the diameter line going across the bottom of the figure.

http://mathcentral.uregina.ca/qq/database/qq.09.10/h/keith2.html

So the perimeter of the semicircle is

[one half the perimeter of the entire circle]  + [the diameter]
[ . . . . . . . . . . . . . ..`(1)/(2)(43.99)`. . . . . . . . . . . . . .]`+`[. . . . . 14 . . . .]

`C_"semicircle"= (1)/(2)(43.99) + 14`

`C_"semicircle"=21.99 + 14`

`C_"semicircle"=35.99  m` `larr` the perimeter of the semicircle