Perimeter and Area

Perimeter and area are two important and fundamental mathematical topics.

They help you to quantify physical space and also provide a foundation for more advanced mathematics found in algebra, trigonometry, and calculus.


Question 1 of 2

1. Find the perimeter of this rectangle.

Use this formula
P=2l + 2w

Question 1 of 2

Question 2 of 2

2. Find the area of this rectangle.

Use this formula.

Area = w × h

w = width
h = height


Question 2 of 2


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The transcript of the video.
A perimeter is a measurement of the distance around a shape and area gives us an idea of how much surface the shape covers.

Knowledge of area and perimeter is applied practically by people on a daily basis, such as architects, engineers, and graphic designers, and is math that is very much needed by people in general. Understanding how much space you have and learning how to fit shapes together exactly will help you when you paint a room, buy a home, remodel a kitchen, or build a deck.


The perimeter of a two-dimensional shape is the distance around the shape. You can think of wrapping a string around a triangle. The length of this string would be the perimeter of the triangle. Or walking around the outside of a park, you walk the distance of the park’s perimeter. Some people find it useful to think “peRIMeter” because the edge of an object is its rim and peRIMeter has the word “rim” in it.

If the shape is a polygon, then you can add up all the lengths of the sides to find the perimeter. Be careful to make sure that all the lengths are measured in the same units. You measure perimeter in linear units, which is one dimensional. Examples of units of measure for length are inches, centimeters, or feet.

Problem:  Find the perimeter of the given figure. All measurements indicated are inches.

P = 5 + 3 + 6 + 2 + 3 + 3

Since all the sides are measured in inches, just add the lengths of all six sides to get the perimeter.
Remember to include units.


Answer:          P = 22 inches

This means that a tightly wrapped string running the entire distance around the polygon would measure 22 inches long.

Problem: Find the perimeter of a triangle with sides measuring 6 cm, 8 cm, and 12 cm.

P = 6 + 8 + 12

Since all the sides are measured in centimeters, just add the lengths of all three sides to get the perimeter.

Answer:           P = 26 centimeters

Sometimes, you need to use what you know about a polygon in order to find the perimeter. Let’s look at the rectangle in the next example.

Problem:   A rectangle has a length of 8 centimeters and a width of 3 centimeters. Find the perimeter.

P = 3 + 3 + 8 + 8

Since this is a rectangle, the opposite sides have the same lengths, 3 cm. and 8 cm. Add up the lengths of all four sides to find the perimeter.

Answer:        P = 22 cm

Notice that the perimeter of a rectangle always has two pairs of equal length sides. In the above example you could have also written P = 2(3) + 2(8) = 6 + 16 = 22 cm. The formula for the perimeter of a rectangle is often written as P = 2l + 2w, where l is the length of the rectangle and w is the width of the rectangle.


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