Triangles: half the rectangle around them
Draw a triangle inside a rectangle with the same base and height, slide its top corner along and see that its area is always half the rectangle, even when the triangle leans over.
Core concept
Area of a triangle = ½ × base × height, wherever the top corner is; its perimeter is the sum of its three sides
Topic: Area and perimeter
Draw a rectangle and cut it along a diagonal: you get two equal triangles, so each is half the rectangle. Any triangle fits inside a rectangle with the same base and the same height, and it always fills exactly half of it, even when its top corner leans out past the end of the base. So the area: How much flat space a shape covers, measured in square units like cm². All key words of a triangle is ½ × base × height. The height is the straight-up distance from the base to the top corner, not the length of a slanting side. The perimeter: The total distance around the edge of a shape. All key words is the distance round the triangle: add its three sides.
What you will learn
- Find the area of a triangle using ½ × base × height.
- Show that triangles with the same base and height have the same area.
- Find the perimeter of a triangle by adding its three sides.
Before you start
- Find the area of a rectangle as length × width.
Materials
- Squared paper, a pencil and a ruler
- Scissors, to cut a rectangle along its diagonal
Equipment
- A set square for drawing the height straight up
Procedure
- Draw a triangle with base 6 cm and height 4 cm, and the rectangle round it.
- Compare the triangle's area with the rectangle's.
- Slide the top corner along, to make a right-angled and then a leaning triangle, and record each.
- Double the height and record again.
How this simulation is simplified
- Lengths are measured in centimetres on a 1 cm grid.