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Estimating the Area of Irregular Shapes

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  • 0:04 New Carpeting
  • 0:31 What Is Area?
  • 1:09 Area of Basic Shapes
  • 2:10 Area of Irregular Shapes
  • 5:07 Lesson Summary
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Lesson Transcript
Instructor: David Karsner
Many shapes have formulas that allow you to find the area quickly. Some shapes are irregular and do not fall neatly into these formulas. This lesson will cover how to find the area of different, irregular shapes.

New Carpeting

Well, the good news is that you are getting new carpeting in your bedroom. The bad news is that your bedroom is an odd shape, and you don't know how much carpeting it will take.

Bedroom Floor Plan
BedroomFloorPlan

What is Area?

Area is the amount of space inside a shape. Imagine that you have a rectangle and a lot of one-inch squares cut out of construction paper. The number of one-inch squares it takes to completely cover the rectangle with no gaps or overlaps is the area of the rectangle. If it took 42 of those one-inch squares to cover the rectangle, that rectangle would have an area of 42 square inches. Area is always measured in square units, such as square inches, square centimeters, square feet, etc. It is also written as 42 sq. inches, or 42 in2.

Area of Basic Shapes

To find the area of a shape, you could cover it with a lot of squares and then count, but that takes a lot of time. There is a quicker way. Formulas allow you to find the area of common shapes quickly. All you have to do is take a couple of measurements and do some computations. Many times the measurements will have been given to you, making it even easier. One of the simplest formulas is the area of a rectangle. The area of a rectangle is length times width (A = lw). If you know the length and width of the rectangle, you multiply the two together to get the area.

Other common shapes have formulas as well. The formula for finding the area of a triangle is area = base times height divided by 2 (A = bh / 2), and the formula for finding the area of a circle is area = 3.14 times radius squared (3.14r2).

Areas of Basic Shapes
AreaChart

Area of Irregular Shapes

Many shapes are not basic shapes like rectangles, triangles, and circles that we have formulas for. There are times when you need to find the area of a shape that is not a regular shape. One method for finding the area of an irregular shape is to divide the shape into smaller shapes which you do have the formula for. Then you find the area of all of the smaller shapes and add all of your areas together.

Dividing Irregular Shapes into Common Ones
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Let's take a look at this example of a pentagon. We don't have a formula to find the area of a pentagon; however, if we divide the pentagon into a rectangle and a triangle, we do have formulas for both of those shapes. In this case, the rectangle is 10 x 12, and therefore it has an area of 120 ft2. The triangle has a base of 10 and a height of 3, and using our formula, (10 x 3) / 2 is 15 ft2. Adding these two areas together, we find the area of our pentagon is 135 ft2.

At times, you're finding the area of an irregular shape that appears to be a shape inside of another shape. In this case, you're taking away some area. You would subtract the area of the inside shape from the area of the outside shape.

Irregular Shapes Requiring Subtraction
CircleRectangle

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