Write the formula for the area of a semicircle.

Substitute the area.

Multiply by 2, and divide by pi on both sides.

The equation becomes:

Square root both sides and factor the right side.

The diameter is double the radius.

The circumference is half the circumference of a full circle.

The perimeter is the sum of the diameter and the half circumference.

The answer is:  

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:

where a is the length of any side. Now, to find the length of one side, we will solve for a. 

We know the perimeter of the hexagon is 90in. So, we will substitute and solve for a. We get

Therefore, the length of one side of the hexagon is 15in.

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is

where a is the length of any side. To find the length of one side, we solve for a. 

Now, we know the perimeter of the hexagon is 138cm. So, we can substitute and solve for a. We get

Therefore, the length of one side of the hexagon is 23cm.

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:

where a is the length of any side. Now, to find the length of one side, we will solve for a.

We know the perimeter of the hexagon is 126in. So, we will substitute and solve for a. We get

Therefore, the length of one side of the hexagon is 21in.

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is

where a is the length of any side. To find the length of one side, we solve for a.

Now, we know the perimeter of the hexagon is 198cm. So, we can substitute and solve for a. We get

Therefore, the length of one side of the hexagon is 33cm.

Examine the bottom figure, in which the bottom two sides have been connected. Note that the figure is now a rectangle cut out of a rectangle, and, since the opposite sides of a rectangle have the same length, we can fill in some of the side lengths as shown:

Three of the sides are of unknown length, but it is not necessary to know the values. Since opposite sides of a rectangle are of the same length, it can be deduced that 

.

The perimeter of the figure is equal to the sum of the lengths of its sides, which is

Substituting 100 for :

The semicircle perimeter will include half the circumference of a regular circle as well as the diameter.

Given the radius, we can first determine the circumference of the half circle.

The diameter is double the radius, or .

Sum the circumference and the diameter to get the perimeter.

The answer is:  

To find the perimeter of a hexagon, we will use the following formula:

where a is any side of the hexagon. Because a hexagon has 6 equal sides, we can use any of them in the formula. 

Now, we know the hexagon has a side of 9cm. So, we can substitute. We get

To find the perimeter of a pentagon, we will use the following formula:

where a is the length of any side of the pentagon. Because a pentagon has 5 equal sides, we can use any of those sides in the formula.

Now, we know the pentagon has a side of 8in. So, we can substitute. We get

This problem is asking us to solve for how much fencing Joe requires to fence his backyard. In order to solve for this, we must find the perimeter of the backyard. The perimeter is a sum of the sides of a shape - or in this case, Joe's backyard. This makes sense to use, because fences usually line the outside - or the perimeter - of a backyard. 

Perimeter is solved for through , where l is length and w is width. Although this problem does not explicitly state which value corresponds to width or length, it doesn't matter in this problem as both value will be multiplied by