Learn

Perimeter, Area, and Volume

Many people will tell you that they never use most of the math they learned in school once they are out of school. I don't know how this is possible! Even if you do not go into a career that involves a lot of math, you will still use math in your everyday life. In this section, we are going to look at uses of perimeter, area, and volume.

Suppose that you want to add a pool in your backyard. You will most likely have to hire someone to do some, if not all, of the work. It is not wise to be totally ignorant of what is going on when you are doing this. Even if you are not going to do the work yourself, you need to know how to check the figures in the estimates that you receive. You should also get estimates from more than one contractor.

If you are going to put in a pool, you will need to decide on its location and the size that you would like to install. You will also need to decide if it is going to be an above-ground pool or an in-ground pool and how much concrete or decking you would like around it, as well as what type and how much fencing will be needed to surround it for safety.

You decide on an in-ground pool surrounded by concrete. Find how many cubic yards of concrete will be needed if the concrete is to be poured 4 inches thick. Also, determine how many linear feet of fencing will be needed if you only fence in the three sides not attached to the house.

backyard of house with concrete measurements 48 feet long and 36 feet wide and the pool measurements 36 feet long and 18 feet wide

Concrete

Concrete is sold in cubic yards. All of our measurements will need to be converted to yards. The dimensions in the drawing are in feet. To convert to yards, divide each measurement by 3 because there are 3 feet in 1 yard.

converting feet measurements to yards, 36/3 = 12 yards, 18/3 = 6 yards, 48/3 = 16 yards


backyard of house with concrete measurements 16 yards long and 12 yards wide and the pool measurements 12 yards long and 6 yards wide


To find the area to be covered by concrete, we will find the total area and subtract the area of the pool.

Total Area

  • A = lw
  • A = 16(12)
  • A = 192 yards

Total Area of Pool

  • A = lw
  • A = 12(6)
  • A = 72 yards

Total Area of Concrete

  • 192 − 72 = 120 yards2

To find the cubic feet of concrete we will have to multiply the area by the thickness or depth we want the concrete to be poured (which is 4 inches thick). We will also have to change this measurement to yards because it is given in inches. We will divide it by 36 because there are 36 inches in a yard.

converting inches to yards 4/36 = 1/9 yard

The concrete will be 1⁄9 of a yard thick.

1/9 (120) = 13 1/3 yards^3 of concrete needed

You will need 13 ⅓ yards3 of concrete.

You will most likely have to round this up to 14 yards3 when ordering the concrete.

 

Fencing

We normally fence the entire perimeter of an area but, in this case, we can use the back wall of the house as part of the barrier. We will use the original image, which has the dimensions given in feet, because we want to find how many linear feet we need to build the fence.

backyard of house with concrete measurements 48 feet long and 36 feet wide and the pool measurements 36 feet long and 18 feet wide

 

The house will take the place of one length.

P = 2l + 2w

P = l + 2w

P = 16 + 2(12)

P = 16 + 24

P = 40

You will need 40 linear feet of fencing.

 

Pool

backyard of house with concrete measurements 48 feet long and 36 feet wide and the pool measurements 36 feet long and 18 feet wide

You are going to have to fill the pool with water once it is installed. It is important to know how much water it will hold in order to keep up the needed chemicals. Let's say that the pool has an average depth of 6 feet.

V = lwh

V = (36)(18)(6)

V = 3,888 feet3

The pool does have a volume of 3,888 feet3 but we are talking about water in this problem and it is measured in liquid units. Therefore, we will need to convert from cubic feet to gallons. There are 7.48052 gallons in each cubic feet so we will multiply this number times the number of cubic feet the pool holds.

7.48052 (3,888) = 29,084.2618 gallons of water

There are 29,084.2618 gallons of water in the pool if it is filled to the very top.

 

Carpet

Once you have put in the pool, you may find that you are having a good bit more company and that you want to spruce up the inside of your house some. You decide to start in the living room. You want to paint it and to lay some new carpet. The dimensions of the room are 15x18 feet with walls that are 8 feet tall.

Carpet is normally sold by square yard so you will need to convert your measurements to yards.

15/3 = 5 yards ; 18/3 = 6 yards

You will then need to find the area of the room to be carpeted.

A = lw

A = 5(6)

A = 30 yards2

You will need 30 square yards of carpet.

 

Paint

For these renovations, you will also need to know the area of the walls so that you will know how much paint to buy. To find the area of the walls you can multiply the perimeter of the room by the height of the walls.

P = 2l + 2w

P = 2(15) + 2(18)

P = 30 + 36

P = 66

Area = 8(66)

Area = 528 feet2

The wall area is 528 square feet.

If one gallon of paint will cover 400 square feet of wall space, how many gallons of paint do you need to buy?

528 ÷ 400 = 1.32 gallons

You can generally buy paint in gallons or pints so you will need to round up to the next gallon and buy 2 gallons for this job.