The idea in brief. A triangle on one side of a rectangle with its tip anywhere on the opposite side keeps the same base and the same height. Height is the distance across from the base to the tip. Moving the tip changes the shape and not the area. In the lesson. Half of base times height is half the area of the box.
Lesson video, with the working
Triangles inside a rectangle
4 min 28 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
How do you solve triangle in a rectangle area questions in P6?
Many Primary 6 composite figures draw a triangle inside a rectangle.
What your child learns here
Many Primary 6 composite figures draw a triangle inside a rectangle. Knowing which length is the base and which is the height turns these into short questions, and lets a child work backwards from an area to a length.
Use area of triangle = ½ × base × height, with the height measured at a right angle to the base.
See that a triangle standing on a whole side of a rectangle, with its tip on the opposite side, has half the rectangle's area wherever the tip sits.
Use only the part of the side the triangle stands on when its base is shorter than the rectangle.
Work backwards: double the triangle's area, then divide by the base to find the height.
Does the answer make sense?
A triangle inside a rectangle can never cover more than half of it, and covers exactly half when it stands on a whole side with its tip on the opposite side. So when your child finds a side from a triangle's area, the rectangle with that side must be at least double the triangle.
How to practise these questions
Basic questions train the fact that a triangle on a whole side of a rectangle, with its tip on the opposite side, is half the rectangle. Intermediate questions add the reverse, where a triangle's area is given and a side of the rectangle or square is found. Challenge questions give a square only by its diagonal, overlap two triangles, or finish with a perimeter. If the half-the-rectangle idea is not landing, read the written step-by-step solution.
Questions parents ask
How does my child know which length is the height? The height is the distance from the tip to the base, measured at a right angle to the base. In a triangle inside a rectangle, it is often the rectangle's side that meets the base at a right angle.
Is area of triangle taught in P6? Area of triangle and the ideas of base and height are listed in the MOE syllabus the year before Primary 6. In Primary 6 they are used in composite figures.
Why does the position of the tip not matter? Moving the tip along the opposite side keeps the base and the height the same, so ½ × base × height does not change. Only the triangle's shape changes.
