Area

The area of a triangle is half the area of a rectangle drawn around the outside.

The perpendicular height is also known as the "right angle height". It is at a right angle to the base of the triangle.

The area of a circle is:  $A_{circle_{ }}=\pi r^2$ 

You don't need to understand how this formula is found, but here are some fun videos showing you how it works.

The last video showed you how we found the area of a circle using triangles. Here's how we found it using rectangles.
First, cut up a circle into even pieces, and try to make it fit into a rectangle.

That shape wasn't a very good rectangle. What if we cut it into smaller pieces?

If we managed to cut the circle into super small pieces, it starts to look like a rectangle.

The height is the same as the radius, r. The length around the outside of the circle is the circumference 2πr. So the length of the rectangle is half of that:πr. Therefore:

A = length x width.

A = r x πr

A = πr²