Area of Polygons Study Guide

Practice problems for these concepts can be found at: Area of Polygons Practice Problems

Introduction to the Area of Polygons

Lesson Summary

In this lesson, you will learn how to use formulas to find the areas of rectangles, parallelograms, triangles, and trapezoids. You will also learn how to use the formulas to work backward to find missing lengths of polygons.

People often confuse area and perimeter. As you learned in Lesson 12, perimeter is the distance around an object. In this lesson, you'll work with area, which is the amount of surface covered by an object. For example, the number of tiles on a kitchen floor would be found by using an area formula, while the amount of baseboard used to surround the room would be found by using a perimeter formula. Perimeter is always expressed in linear units. Area is always expressed in square units. You can not measure the amount of surface that is covered by an object by simply measuring it in one direction, you need to measure the object in two directions, like a square. A flat surface has two dimensions: length and width. When you multiply a number by itself, the number is said to be squared. In the same way, when two units of measurement are multiplied by each other, as in area, the unit is expressed in square units. By looking at a tiled floor, it is easy to see that area refers to how many squares it takes to cover a surface.

Finding the Area of a Rectangle

For a rectangle, the base can be any side. The base length is represented by b. The sides perpendicular to the base are referred to as the height. The height is referred to as h. The base is often called the length, l, and the height is often called the width, w. Length, l, and width, w, are used in the same manner as base, b, and height, h. This book uses base and height.

Here is a useful theorem you can use to find the area of a rectangle.

Examples:

Find the area of each rectangle.

Finding the Length of an Unknown Side of a Rectangle

You can also use the area formula for a rectangle to find the length of an unknown side if you know the area.

Examples:

For each rectangle, find the length of the indicated sides.

Finding the Area and Unknown Sides of a Parallelogram

Any side of a parallelogram can be called the base. The height is the length of the altitude. The altitude is a segment perpendicular to the base.

Draw an altitude of a parallelogram. Cut along the altitude to separate the parallelogram into two pieces. Fit the two pieces together to form a rectangle. You'll find that the base and height of the rectangle coincide with the base and altitude of the parallelogram.

Using this information, can you predict the area formula for a parallelogram? Take a moment to make your prediction, then look at the following theorem.

Note that the 5 cm measurement is unnecessary information for this problem. Recall that the base and height must be perpendicular to each other.

Finding the Area and Unknown Sides of a Triangle

Look at the following figures and try to predict the area formula for a triangle.

Now see if your prediction is correct by reading the theorem below.

Examples:

Find the area.

Finding the Area and Unknown Sides of a Trapezoid

Can you predict the area formula for a trapezoid? Look at these figures:

Examples:

Find the area or indicated length.

Practice problems for these concepts can be found at: Area of Polygons Practice Questions.