Workplace Math and PLAR Prep

Measurement

Area of a rectangle or square

In this section we will learn how to calculate the area of a square and rectangle. We have used inches and feet in this section as most carpenters and building stores still use the imperial system.

Area of a square or rectangle = Length x Width A = L x W

Example: Imagine you're planning to buy new carpet for your home. You're going to put down carpet in the living room, bedroom, and hallway, but not in the bathroom. The diagram beside shows you the dimensions of each room.

Problem: Calculate the square footage of all the space except the bathroom. Most contractors work with the imperial system when calculating area. Most materials come in square feet.

Solution:

Step 1: Start by figuring the total area of the floor plan. A = L x W L = 7 feet + 5 feet + 10 feet = 22 feet W = 7 feet + 5 feet = 12 feet A = 22 feet x 12 feet = 264 square feet

Step 2: Calculate the area of the bathroom. A = 7 feet x 5 feet = 35 square feet

Step 3: Subtract the total area from the area of the bathroom. 264 square feet – 35 square feet = 229 square feet

The square footage of all the space except the bathroom is 229.

Now it's your turn...

Tim and Susie want to do some renovations to their home. They would like to put tile in the kitchen, carpet in the living room and bedrooms and laminate in the bathroom and hallway. They also want to paint their deck.

Use the image above to answer the following questions:

1. What is the area of the kitchen?

2. Each tile is one square foot. How many tiles would they need for the kitchen (they will need 10% more than what is needed to account for breakage). Round your answer to the nearest whole number.

3. Each tile costs $4.59. How much will it cost to tile the kitchen?

4. What is the combined area of the living room and bedrooms?

5. How much carpet will they need if they add 10% onto your total square footage? Round your answer to the nearest whole number.

6. The cost for carpet is $3.19 per square foot. How much will it cost for materials to carpet the living room and bedrooms?

7. What is the area of the bathroom and hallway combined?

8. How much laminate will they need if they add 10% onto your total square footage?

9. Laminate comes in 4 square foot pieces. How many pieces will they need to do the bathroom and hallway? Round to the nearest piece.

10.Each 4 square foot piece costs $4.15. How much will it cost to put laminate in the bathroom and hallway?

11.What is the area of the deck?

12. How much paint will they need for their deck if a 1 gallon can of paint covers 350 square feet and they need to do 2 coats?

13.Each gallon of paint costs $45.89. How much will it cost to paint their deck?

14.They have hired a contractor to do the work. He has estimated that it will take 50 hours to do all the installation and painting. He charges $45.00 per hour. How much will it cost for the labour?

15. How much will it cost Tim and Susie for all their renovations?

Click on the arrow to compare your answers -------->

1) 13" x 16" = 208 square feet

2) 208 x 0.10 = 20.8; 20.8 + 208 = 228.8 or 229 tiles

3) 229 x $4.59 = $1051.11

4) (15 x 16) + (10 x 10) + (10 x 12) = 460 square feet

5) 460 x 0.10 = 46; 460 + 46 =506 square feet

6) 506 x $3.19 = $1614.14

7) (4 x 28) + (10 x 6) = 172 square feet

8) 172 x .010 = 17.2; 172 + 17.2 =189.2 or 189 square feet

9) 189/4 = 47.25 or 47 pieces

10) 47 x $4.15 = $195.05

11) 9 x 28 = 252 square feet

12) 2 gallons

13) $91.78

14) $2250

15) $5202.08

Area of a circle

A circle's radius is one half of its diameter, or one half of what you get if you measure all the way across its widest part. "Squaring" (^2) something means you multiply it by itself.

Pi is a number that roughly equals 3.14159; we usually round it off to 3.14.

Area of a circle: Area = Pi x radius^2 A = x r^2

Example:

If your living room has a semi-circular alcove as in this floor plan you'll need to use this additional equation to figure out its area.

Problem: What is the square footage of the living room?

Solution:

Step 1: To figure the radius of your alcove (the number you'll need to plug into the equation) you'll divide its diameter in half. Its diameter is the same as the width of the living room: 12 feet. Half of that is its radius: 6 feet.

Step 2: A = 3.14 x (6 feet x 6 feet)

A = 113 square feet (rounded to the closest square foot)

Step 3: If your alcove were a complete circle, it would have an area of 113 square feet. Because it's a half circle, the area is half of 113

113 ÷ 2 = 56.5 square feet.

Step 4: Calculate the rest of the living room 10 feet x 12 feet = 120 square feet. The total square footage is 120 square feet + 56.5 square feet = 176.5 square feet

Now it's your turn...

Directions: Tim and Susie decided to put an addition onto their living room. They added a circular alcove. They need to add carpet to this new section. They also want to buy area rugs for the kitchen, hallway and bathroom. Each area is marked on the diagram.

Answer the questions below.

1. Calculate the area of the new part of the living room. Round your answer to the nearest whole number.

2. How much will the carpet cost for the addition? The carpet costs $3.19 per square foot and they should buy 10% extra to cover any mistakes or mishaps. Round your answer to the nearest whole number.

3. What is the area of the rug in the kitchen? Round your answer to the nearest decimal.

4. What is the area of the rug in the bathroom? Round your answer to the nearest decimal.

5. What is the area of the rug in the hallway?

6. The rugs cost $39.95, $15.95 and $25.89. How much does it cost for all the area rugs?

Check your answers here -------------------------->

1) 88 square feet

2) $308.79

3) 28.3 square feet

4) 12.6 square feet

5) 30 square feet

6) $81.79

Want to learn more about area? Check out the videos below

Next: Perimeter

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