The perimeter is the total distance around the outside of a shape. Since a semi-circle is a circle cut in half, the length of a semicircle's curve is equal to half the perimeter of a full circle with the same diameter. But because the straight line across one side of a semicircle is part of a semicircle’s perimeter, you include the straight line in your calculation. Does this sound complicated? Don't worry. If you know the diameter of a semicircle, you can find its perimeter with the following equation:
Where P is the Perimeter and d is the diameter, the formula is:
P = *d + pi x d/2*
The Diameter and Radius of a Semicircle
To find a semicircle's perimeter, you need to know the semicircle's diameter or radius. The diameter -- d-- of a semicircle is the length of the semicircle's straight side. The radius -- r -- is the distance from the point halfway across a semicircle's straight side to a point on the semicircle's curve.
The radius is the same for all points on the curve. Since the radius is halfway across the straight side, the radius is equal to one half of the diameter. If you know the radius, calculate the diameter by multiplying the radius by two. So, a semicircle with a radius of 4 inches has a diameter of 8 inches.
The number pi is extremely important when doing calculations with circles. What is pi? Pi is defined mathematically as a circle's circumference divided by its diameter. The value obtained from this division is the same for all circles, so pi always has the same value -- around 3.14.
Note that this value is an approximation of pi --- pi can be extended for an infinite number of digits after the decimal point. However, when you're doing basic arithmetic with circles and semicircles, 3.14 is a good enough approximation.
Find the Circumference
If you've worked with circles, you know that the perimeter -- or the circumference -- of a circle is equal to its diameter times pi: pi x d. You can also use this formula to find the length of a semicircle's curve. Remember that a semicircle's curved side is one half the length of the perimeter of the circle with the same diameter.
So, multiply the diameter by pi, and then divide that value by 2:
Curve Length = pi x d/2
Suppose you have a semicircle that has a radius of 7 inches. The radius is one half the length of the diameter, so this semicircle has a diameter of 14 inches. You multiply 14 times pi and divide by two.
Curve Length = (3.14 x 14 inches)/2 Curve Length = 43.96 inches/2 Curve Length = 21.98 inches
So, the curved side of the semicircle has a length of 21.98 inches.
Add the Diameter
The straight side of the semicircle is also part of its perimeter. You add this length to the length of the semicircle's curve. Remember, the straight side of the semicircle includes the length of its diameter.
Straight Length = d
Take the semicircle from the previous example, that has a radius of 7 inches. Since the radius is 7 inches, the diameter is 14 inches. Add this to the length of the curved side -- 21.98 inches - -to get the perimeter.
P = 14 ins + 21.98 inches P = 35.98 inches
So, this semicircle will have a perimeter of 35.98 inches.
You can remember the formula to calculate the perimeter of a semicircle with the following equations:
P = straight length + curve length Curve length = pi x d/2 Straight length = d
Combined, this is the formula to calculate the perimeter of a semicircle.
P = d + pi x d/2