Area is the amount of space inside a shape. It is measured in square units. If you place a shape on a grid, the area is the number of squares that can fit inside the shape.

For a rectangle, you could count the number of squares to find the area. For example, the rectangle below covers 12 squares so the area is 12 square units.

Instead of counting squares, you can also use a formula to find the area of a rectangle. The formula for the area of a rectangle is Area = length x width. For the rectangle above, we could have also multiplied 4 x 3 to find the area.

What would happen if we cut a rectangle in half to form a triangle? What would the new area be?

The area of the rectangle is 12 square units. If the rectangle has been cut in half to form two equal triangles, then each triangle must have 1/2 the area of the rectangle. This means we can take 1/2 of 12 to find the area of the triangle, so the area is 6 square units.

How Do You Find the Area of a Triangle?

There is a formula we can use to find the area of a triangle. It's similar to the formula for the area of a rectangle, except it uses base and height instead of length and width. A triangle takes up half as much space as a rectangle, so there is a 1/2 in the formula.

What if the triangle doesn't look like the one drawn? Sometimes the height isn't one of the sides of the triangle. The base and height of a triangle are always perpendicular to each other, so look for the box that marks the 90 degree angle.

The base can be any of the 3 sides of the triangle. Typically, we pick the side on the "bottom" for the base, but you could rotate your paper and a different side would be on the bottom. It doesn't matter which side you choose for the base, but the height and the base must be perpendicular to each other. The height may be one of the sides of the triangle (if it's a right triangle). The height may be inside the triangle (like the triangle in the middle below), or the height may be outside the triangle (like the triangle on the right below).

Example 1 Find the area of the triangle.

Step 1: Identify the base and height. The base and height must be at a 90 degree angle. This means the base = 12 and height = 10

Step 2: Plug the base and height into the formula for the area of a triangle.

Step 3: Simplify. Take half of 12 first to get 6. Then multiply 6 by 10 to get 60 square units. If you're using a calculator, you can enter .5 for 1/2 or you can multiply the base and height together first and then divide by 2.

Example 2 Find the area of the triangle.

Step 1: Identify the base and height of the triangle. Remember to look for the box that marks the 90 degree angle. The base and height must be perpendicular to each other. This means the base = 15 and the height = 6.

Step 2: Plug the base and the height into the formula for the area of a triangle.

Step 3: Simplify. You can enter .5 for 1/2 if you're using a calculator. Or you could multiply the base and height together first and then divide by 2.