Composite Figures

Lesson 1: Perimeter and Circumference - Composite Figures

   Constructing Knowledge

Not every 2-D shape is a simple rectangle or circle. Some 2-D shapes are actually made up of more than one simple shape. These 2-D shapes are often called composite figures. Calculating the perimeter of a composite figure often requires multiple steps.

To calculate the perimeter of composite figures:

1. Draw and label a diagram (if there isn't one provided).
2. Calculate any missing side lengths, and label them on the diagram.
3. Calculate the total perimeter by adding up all the side lengths.

   Multimedia

A video describing the perimeter of composite figures is provided.

EXAMPLE 1

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An NBA basketball court has an area at each end that is comprised of a rectangle (the key) and a semicircle. The free throw line (width of the rectangle) is 12 feet across and is 19 feet from the baseline (length of the rectangle). The radius of the semicircle is 6 feet. What is the perimeter of the key and semicircle combined?

Solution

Step 1. Draw and label the diagram.



Step 2. Calculate any missing side lengths and then label them on the diagram.

The unknown lengths are the bottom of the rectangle, the left side, and the semi-circle circumference.
The bottom length is 12 feet as it is the same length as the free throw line (rectangle).
The left side length is 19 feet as it is the same length as the right side (rectangle).

The semicircle's length needs to be calculated. It is half the circumference of a circle with radius 6 feet.

\(\begin{align} \text{Circumference}&=\frac{2\pi r}{2} \\ \\ &=\frac{2\times 6\pi\times 6\,\text{ft}}{2} \\ \\ &=18.8\,\text{ft} \end{align}\)



Step 3. Calculate the total perimeter by adding up all the side lengths.

Perimeter	= left side + right side + baseline + semi-circle
	= 19 ft + 19 ft + 12 ft + 18.8 ft
	= 68.8 ft

The perimeter of the basketball key and semi-circle is 68.8 feet.

Notice that the free throw line's length was not used in the perimeter calculation because the measure is inside the shape, rather than part of the shape's perimeter.




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