A triangle inside a rectangle is in the Primary 5 Area of Triangle chapter. The lesson film is the one Mathweave teaches this skill with in Primary 6, and the practice set below is chosen for Primary 5.
Write the rule first: area of a triangle is half of base times height.
The base is A B, 18 centimetres. The height is the shortest distance down to the base, at a right angle: 10 centimetres.
Slide E along the far side. The height never changes, so the area does not change.
Put the numbers in: half of 18 times 10, so 9 times 10 is 90 square centimetres.
To go backwards, double the area and divide by the base: 96 times 2, divided by 16, is 12 centimetres.
Half of base times height is half of the box.
Worked example, step by step
From the lesson: Triangles inside a rectangle
ABCD is a square of side 20 cm. Its diagonals AC and BD are drawn and meet at M. The shaded parts are triangle ABD and triangle ABC. Find the area of the square that is not shaded.
area of the square = 20 × 20 = 400 cm²
area of each shaded triangle = 1/2 × 20 × 20 = 200 cm²
the diagonals meet at the centre, so the doubly shaded part = 400 ÷ 4 = 100 cm²
area shaded = 200 + 200 − 100 = 300 cm²
unshaded area = 400 − 300 = 100 cm²
Ans: The answer is 100 cm².
Practice questions with worked solutions
Question 1 is free to try. The other 8 open in the free trial, each with its full working.
How do you solve triangles inside a rectangle questions in P5?
These questions draw a triangle with its corners on the sides of a rectangle or square.
What your child learns here
These questions draw a triangle with its corners on the sides of a rectangle or square. The rectangle supplies the base and the height, so the Primary 5 area of triangle formula only needs the right two lengths, and it can also be run in reverse.
Find the base on one side of the rectangle, using only the part of that side the triangle stands on.
Take as the height the side of the rectangle that meets that base at a right angle, not a slanting edge of the triangle.
A triangle on a whole side with its tip on the opposite side is half the rectangle, wherever the tip sits.
To find a missing length, double the triangle's area and divide by the base you know.
In a square the base and the height are equal, so one length gives both.
Does the answer make sense?
Triangle AED is a right-angled corner with sides 12 cm and 9 cm, so it is half of a 12 cm by 9 cm rectangle of 108 cm². Half of 108 is 54 cm². The whole rectangle is 20 × 9 = 180 cm², and 54 cm² is less than half of it, as it should be, because AE is shorter than AB.
How to practise these questions
Free Question 1 gives a rectangle ABCD with AB 20 cm and AD 9 cm, puts E on AB so that AE is 12 cm, and asks for the area of triangle AED. The Basic questions train choosing the base and its height and seeing a triangle as half of the rectangle. Intermediate questions run the formula backwards to find a side, including the side of a square. Challenge questions find part of a side, a perimeter, a doubly shaded part, and the area of a square from its diagonal. If your child is stuck, open its worked solution and trace the base and the height in two colours. A multiple-choice Intermediate question shows triangles drawn inside a rectangle and asks which statement about their areas is true, with the reasoning written out.
Questions parents ask
Which length is the height of the triangle? The height runs from the tip straight to the base at a right angle. Inside a rectangle it is usually the side next to the base, such as AD when the base lies along AB.
Why is the triangle half of the rectangle? When the base is a whole side and the tip is on the opposite side, the triangle and the rectangle share the same base and height. Half of base times height is then half the rectangle's area.
Is this part of the Primary 5 syllabus? Yes. The Primary 5 Area and Volume strand lists base and height, the area of a triangle, and composite figures made up of rectangles, squares and triangles, which covers every question here.
