Area of a Triangle

Lesson Plan - Get It!

Audio:

You should already know that area measures the space covering a plane shape.

If you need to review the concepts of area or plane shapes, visit our lessons found under Additional Resources in the right-hand sidebar.

In order to understand how to find the area of a triangle, you need to know how to find the area of a rectangle.

To find the area of a rectangle, you multiply the base by the height:

Now, let's look at our first triangle. Notice that there is also a base and height measurement.

• How can we figure out the area of this triangle, keeping in mind what we know about the area of rectangles?

Look what happens if we copy our triangle, rotate it, and move it to the other side:

We made a rectangle!

We know the area of a rectangle is base multiplied by height (b ⋅ h). Our original triangle is half of this rectangle.

So in order to find the area of a triangle, we will multiply the base by the height and then divide that answer by 2. This is also half of the area of a rectangle.

• However, remember our pizza slice pictured at the beginning of the lesson?

It was a different-shaped triangle. It was not a right triangle.

• Will the formula still work the same?

Just like with the right triangle, let's copy the triangle, rotate it, and move it to the other side.

This time, our triangles did not make a rectangle! They made a parallelogram!

• Do you know how to find the area of a parallelogram?

If not, visit our lesson found under Additional Resources in the right-hand sidebar.

The area of a parallelogram is also base multiplied by height (b ⋅ h)!

So, just like with the right triangle, the area of this triangle will be half of the area of a parallelogram.

The only difference is that the height measurement will not be the length of one of the triangle's sides. The height will always be at a right angle and will measure from the base to the highest point of the triangle.

For a quick recap and everything you just learned, watch Formula for Area of a Triangle - Why? from Amy Cotten:

Now, you are ready to find the area of our pizza slice!

Visit the Got It? section to show what you learned!