GED Math - Perimeter and Sides

A hexagon has a perimeter of 138cm. Find the length of one side.

$23\text{cm}$

$22\text{cm}$

$19\text{cm}$

$21\text{cm}$

$18\text{cm}$

Explanation

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

$138\text{cm} = 6a$

$\frac{138\text{cm}}{6} = \frac{6a}{6}$

$23\text{cm} = a$

$a = 23\text{cm}$

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

A hexagon has a perimeter of 198cm. Find the length of one side.

$33\text{cm}$

$32\text{cm}$

$29\text{cm}$

$31\text{cm}$

$28\text{cm}$

Explanation

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

$198\text{cm} = 6a$

$\frac{198\text{cm}}{6} = \frac{6a}{6}$

$33\text{cm} = a$

$a = 33\text{cm}$

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

A hexagon has a perimeter of 126in. Find the length of one side.

$21\text{in}$

$20\text{in}$

$18\text{in}$

$22\text{in}$

$9\text{in}$

Explanation

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

$126\text{in} = 6a$

$\frac{126\text{in}}{6} = \frac{6a}{6}$

$21\text{in} = a$

$a = 21\text{in}$

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

A hexagon has a perimeter of 90in. Find the length of one side.

$15\text{in}$

$20\text{in}$

$18\text{in}$

$22\text{in}$

$9\text{in}$

Explanation

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

$90\text{in} = 6a$

$\frac{90\text{in}}{6} = \frac{6a}{6}$

$15\text{in} = a$

$a = 15\text{in}$

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

Find the perimeter of a hexagon with a side of length 9cm.

$54\text{cm}$

$45\text{cm}$

$36\text{cm}$

$63\text{cm}$

$18\text{cm}$

Explanation

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

$P = 6(9\text{cm})$

$P = 54\text{cm}$

Find the perimeter of a pentagon with a side of length 8in.

$40\text{in}$

$48\text{in}$

$32\text{in}$

$56\text{in}$

$64\text{in}$

Explanation

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

$P = 5(8\text{in})$

$P = 40\text{in}$

Joe has a rectangular backyard. Its dimensions are by . If he wants to put up fencing around the perimeter, how much fencing will he need?

feet

Explanation

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

What is the perimeter of a semicircle with a radius of 4?

$4\pi +8$

$4\pi +4$

$8\pi +4$

$8\pi +2$

$8\pi +8$

Explanation

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.

$C_{semi} = \frac{1}{2}(2\pi r) = \pi r = 4\pi$

The diameter is double the radius, or .

Sum the circumference and the diameter to get the perimeter.

The answer is: $4\pi +8$

What is the perimeter of a square with a length of inches?

inches

Not enough information

inches

Explanation

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.

Jill would like to create a small pen for her fostered kittens. She plans on making an equilateral triangular shaped pen with only feet of fencing at her disposal. What is the greatest whole number side length the pen can have?

Explanation

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.