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 

This problem asks for us to solve for the perimeter of a square that has a length of  inches. The perimeter can be solved for using , where w means width and l means length. 

In this kind of problem, it's important to remember that squares have 4 equal sides. This means that their lengths equal the width - therefore, it can be misleading to think there isn't enough information. 

Therefore, the square has a perimeter of  inches. 

The problem states that Jill wants to make a pen in the shape of an equilateral triangle. This means the triangle will have three equal sides. With only  feet of fencing, she wishes to make the largest triangle possible. In order to solve for the longest possible whole number length of the triangle pen, we must first utilize some concepts associated with perimeter. 

Perimeter is the sum of all sides. This means that with  feet of fencing, the sum of the three sides cannot exceed  feet. Using this information, we can solve for the maximal side length:

if we set up an equation where all three sides are summed, we can set it equal to , keeping in mind that this is the limit. But we must also keep in mind that s cannot be a decimal number - it must be a whole number. 

Because we are restrained by  feet, we must round the value for s down. This would entail that the side of the pen can be  feet maximum. 

 is a right triangle with legs ; its area is half the product of its legs, which is

 is a right triangle with legs 

and

 ;

its area is half the product of its legs, which is

The shaded region is the former triangle removed from the latter triangle; its area is the difference of the two: .

This region is therefore

 of .

 is a right triangle with legs ; its area is half the product of its legs, which is

 is a right triangle with legs 

and

 ;

its area is half the product of its legs, which is

The shaded region is the former triangle removed from the latter triangle; its area is the difference of the two: .

A hexagon has six sides; a regular hexagon with perimeter 36 has sidelength 

.

A regular hexagon can be divided into six triangles, each of which can be easily proved equilateral, as seen in the diagram below:

Each equilateral triangle has sidelength 6, so each has area

.

The total area of the hexagon is the area of six such triangles: