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Finding the Area of Irregular Figures

Media Type:
Video

Running Time: 3m 44s
Size: 5.0 MB

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Area is the measure of the surface inside a flat figure. Area is measured in square units. Partition irregular figures into regular shapes to find their area.

These resources are part of KET's Measurement and Geometry collection.

This video segment originally appeared in KET’s GED Connection series.

Background Essay

To tile a floor, you have to know how much area there is to be covered. Area is the measure of the surface inside a flat figure. Area is measured in square units. How do you find the surface area of a floor? You could cut a square foot out of cardboard and see how many times it will fit in the space. But instead, you can measure the length and width of the room and multiply. We express this as a formula:

• Area = length X width

A square is simply a rectangle with sides that are the same length. You can measure one side and multiply by four, but you can also use the formula for finding the area of a square:

• Area =side2

Rectangles and squares are “regular” shapes, but not all shapes are regular. “Irregular” shapes are a combination of several shapes. To find the area of an irregular shape, you will need to use logic and common sense to partition the shape into regular shapes that can be measured.

Discussion Questions

• How would you figure out the square footage of your home? It may be helpful to sketch a diagram.
• What irregular shapes do you see in the classroom? How would you partition and measure? Is there more than one way?

Teaching Tips

Have learners work in teams to draw irregular shapes. They must be able to explain how to partition the shape to determine area. But first, have them trade drawings with other teams to see if others can figure out how to partition. Encourage them to have fun and be creative with this exercise!

Have learners draw a regular or irregular figure and label it with measurements. Then have them describe the figure to another learner who must make as accurate a sketch as possible from the description.

Have learners sketch a diagram to help them solve for area of the following problem featured on p. 145 of the GED Connection “Mathematics” workbook:

The Park family is planning to carpet their family room, which measures 18 by 24 feet. They will not need to carpet the fireplace hearth, a 3-ft by 6–ft area centered on one of the 18-ft walls. How many square yards of carpet will they need?

Step 1. Sketch a diagram of the family room floor.

Step 2. Figure the total area of the room (18 X 24 = 432 sq ft) and subtract the floor area covered by the hearth (3 X 6 = 18 sq ft): 432 sq ft – 18 sq ft = 414 sq ft.

Step 3. Convert 414 square feet to square yards (9 sq ft = 1 sq yd).

Standards

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