Perimeter

Perimeter is the distance around the outside of a shape. It is the sum of all the sides of a closed figure.

Formulas for Perimeter

The formulas for finding the perimeter of some common shapes are:

1. Rectangle: \( P = 2l + 2w \) where \( l \) is the length and \( w \) is the width
2. Square: \( P = 4s \) where \( s \) is the length of one side
3. Triangle: \( P = a + b + c \) where \( a \), \( b \), and \( c \) are the lengths of the three sides
4. Circle: \( P = 2\pi r \) where \( r \) is the radius and \( \pi \) is a constant approximately equal to 3.14

Units of Perimeter

The units of perimeter are the same as the units of the individual sides. For example, if the sides are measured in centimeters, the perimeter will be in centimeters.

Example Problems

1. Find the perimeter of a rectangle with length 5 cm and width 3 cm.

Using the formula \( P = 2l + 2w \), we get \( P = 2(5) + 2(3) = 10 + 6 = 16 \) cm. Therefore, the perimeter is 16 cm.

2. Find the perimeter of a square with side length 7 m.

Using the formula \( P = 4s \), we get \( P = 4(7) = 28 \) m. Therefore, the perimeter is 28 m.

Study Guide

When finding the perimeter of a shape, remember to add up the lengths of all the sides. Use the appropriate formula for the specific shape. Pay attention to the units of measurement and make sure to include them in your final answer.

Practice problems:

1. Find the perimeter of a rectangle with length 8 cm and width 4 cm.
2. Find the perimeter of a triangle with side lengths 5 cm, 7 cm, and 9 cm.
3. Find the perimeter of a circle with radius 10 m (use \( \pi = 3.14 \)).

Remember, the key to mastering perimeter is practice! Good luck!