Area of triangles and parallelograms

Hello, and welcome to Myriora Maths! We know how to find the area of a rectangle. But what about a slanted shape, or a triangle? The trick is to cut and move pieces. Let's see!

Here's a parallelogram. Cut a triangle off one end, and slide it to the other end. Now it's a rectangle! So the area of a parallelogram is the base times the height.

Careful: the height is straight up, at a right angle to the base. It's not the slanted side.

Now a triangle. Put a copy of it next to itself, turned round, and you get a parallelogram. So a triangle is exactly half of that. The area of a triangle is half of the base times the height.

This triangle has a base of eight centimetres and a height of five centimetres. Eight times five is forty. Half of forty is twenty square centimetres.

Let's try one together. A parallelogram has a base of seven centimetres and a height of four centimetres. What is its area? Say it out loud!

Base times height: seven times four is twenty-eight square centimetres!

Here's a question that catches lots of people. This triangle has a base of six, a slanted side of five, and a height of four. Some people multiply six by five. But the slanted side isn't the height! Use the height: six times four is twenty-four, and half is twelve.

Your turn! A triangle has a base of ten centimetres and a height of six centimetres. What is its area? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Ten times six is sixty. Half of sixty is thirty square centimetres!

Quick review. A parallelogram can be cut and moved into a rectangle: base times height. A triangle is half of a parallelogram: half of base times height. And the height is always at a right angle to the base. See you next time!