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For each item, state whether you would use linear, square, or cubic measure:

amount of carpeting needed in a room

extension cord length

amount of sand in a sandbox

length of a curtain rod

amount of flour in a canister

size of the roof of a doghouse.

Solution

You are measuring how much surface the carpet covers, which is the area. square measure
You are measuring how long the extension cord is, which is the length. linear measure
You are measuring the volume of the sand. cubic measure
You are measuring the length of the curtain rod. linear measure
You are measuring the volume of the flour. cubic measure
You are measuring the area of the roof. square measure
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Determine whether you would use linear, square, or cubic measure for each item.

amount of paint in a can height of a tree floor of your bedroom diameter of bike wheel size of a piece of sod amount of water in a swimming pool

  1. cubic
  2. linear
  3. square
  4. linear
  5. square
  6. cubic

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Determine whether you would use linear, square, or cubic measure for each item.

volume of a packing box size of patio amount of medicine in a syringe length of a piece of yarn size of housing lot height of a flagpole

  1. cubic
  2. square
  3. cubic
  4. linear
  5. square
  6. linear

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Many geometry applications will involve finding the perimeter or the area of a figure. There are also many applications of perimeter and area in everyday life, so it is important to make sure you understand what they each mean.

Picture a room that needs new floor tiles. The tiles come in squares that are a foot on each side—one square foot. How many of those squares are needed to cover the floor? This is the area of the floor.

Next, think about putting new baseboard around the room, once the tiles have been laid. To figure out how many strips are needed, you must know the distance around the room. You would use a tape measure to measure the number of feet around the room. This distance is the perimeter.

Perimeter and area

The perimeter    is a measure of the distance around a figure.

The area    is a measure of the surface covered by a figure.

[link] shows a square tile that is 1 inch on each side. If an ant walked around the edge of the tile, it would walk 4 inches. This distance is the perimeter of the tile.

Since the tile is a square that is 1 inch on each side, its area is one square inch. The area of a shape is measured by determining how many square units cover the shape.

A 5 square by 5 square checkerboard is shown with each side labeled 1 inch. An image of an ant is shown on the top left square.
Perimeter = 4 inches Area = 1 square inch
When the ant walks completely around the tile on its edge, it is tracing the perimeter of the tile. The area of the tile is 1 square inch.
Doing the Manipulative Mathematics activity Measuring Area and Perimeter will help you develop a better understanding of how to measure the area and perimeter of a figure.

Each of two square tiles is 1 square inch. Two tiles are shown together.

What is the perimeter of the figure?

What is the area?

A checkerboard is shown. It has 10 squares across the top and 5 down the side.

Solution

The perimeter is the distance around the figure. The perimeter is 6 inches.

The area is the surface covered by the figure. There are 2 square inch tiles so the area is 2 square inches.

A checkerboard is shown. It has 10 squares across the top and 5 down the side. The top and bottom each have two adjacent 1 inch labels across, the sides have 1 inch labels.
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Practice Key Terms 6

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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