Primary 5 Area of Triangle Study Guide
Primary 5 Area of Triangle in five short steps, from choosing a base and its height to figures made of several shapes. Each step has a figure to turn, cut or move, and worked examples follow.
Start here
How do you find the area of a triangle?
A triangle has half the area of a rectangle with the same base and height.
So area of triangle = 1/2 × base × height. The base is any side your child chooses. The height is the line from the opposite corner that meets the base at a right angle, and it can fall outside the triangle. A sloping side is not the height.
In this chapter, your child learns to:
- name the height that goes with a chosen base;
- find the area of a triangle with 1/2 × base × height;
- split a figure into rectangles, squares and triangles;
- find a triangle drawn in a rectangle, or a side from its area;
- add two overlapping shapes, then subtract the shared part once.
Base 10 cm, height 7 cm, at a right angle
Rectangle: 10 × 7 = 70 cm²
Triangle: 1/2 × 10 × 7 = 35 cm²
Step 1
Base and height of a triangle
The base is a side you choose; the height follows it. Any of the 3 sides can be the base. The height starts at the corner the base does not touch and meets the base at a right angle. If it cannot land between the two ends, extend the base: the height is then outside the triangle, and it is still the height.
Tap a base
Base AC · Height BD
In triangle PQR, QR is extended to S, and PS meets it at a right angle. QT meets PR at a right angle. QR is the base. Which line is the height?
Step 2
Area of a triangle: 1/2 × base × height
Two equal triangles make one rectangle, so each is half. Take an equal copy of the triangle and turn it to meet the first. Cut along the height and move the end piece into the gap: the two triangles become a rectangle, base times height. One triangle is half of that. The rule is the same when the height is outside the triangle or the base is upright.
Tap Next step
Triangle JKL has base KL = 12 cm. JH meets KL at a right angle and is 8 cm. Find its area.
- Area of 2 triangles = 12 × 8 = 96 cm²
- Area of triangle = 1/2 × base × height
- Area of triangle JKL = 1/2 × 12 × 8 = 48 cm²
Triangle ABC has base BC = 14 cm. BC is extended to D, and AD meets it at a right angle. AD = 6 cm and AC = 10 cm. Find the area of triangle ABC.
Step 3
Area of composite figures with triangles
Split the figure into shapes you know, and give each part its own working. Find any missing length on a line of its own first: a length printed along the whole figure may not belong to the triangle. Each triangle needs its own base and height. Add the parts that make up a figure; subtract a part that has been cut from a whole.
Tap Next step
The figure is made up of rectangle ABED and triangle BCE. AB = 12 cm, AD = 8 cm and DC = 18 cm. Find its area.
- DE = AB = 12 cm
- EC = 18 − 12 = 6 cm
- Area of rectangle = 12 × 8 = 96 cm²
- Area of triangle = 1/2 × base × height
- Area of triangle BCE = 1/2 × 6 × 8 = 24 cm²
- Area of figure = 96 + 24 = 120 cm²
WXYZ is a rectangular card with WX = 16 cm and XY = 10 cm. V is on WX with WV = 6 cm. Triangle WVZ is cut off. What area of card is left?
Step 4
Triangles inside a rectangle
Slide the tip along the far side and the area stays the same. When a triangle stands on one side of a rectangle and its tip is on the opposite side, its height is the rectangle's other side. Moving the tip never makes the height longer or shorter, so the area does not change. To go back the other way, double the area, then divide by the base.
Tap a dot
ABCD is a rectangle with DC = 16 cm and BC = 11 cm. E is a point on AB. Find the area of triangle DCE.
- Area of triangle = 1/2 × base × height
- Base = DC = 16 cm, height = BC = 11 cm
- Area of triangle DCE = 1/2 × 16 × 11 = 88 cm²
A triangle stands on a 12 cm side of a rectangle, with its tip on the opposite side. The triangle's area is 60 cm². What is the breadth of the rectangle?
Step 5
Overlapping shapes: area covered and shared part
Area covered is both shapes minus one shared part. The shared part is inside both shapes. On the paper it is there once, but adding the two shapes counts it twice, so subtract it once. When the area covered is given instead, the shared part is the two shapes minus the area covered.
Tap Add A
Two identical rectangles, each 10 cm by 6 cm, overlap in a strip 3 cm long. Find the area they cover.
- Area of A = 10 × 6 = 60 cm²
- Area of A and B = 60 + 60 = 120 cm²
- Shared part = 3 × 6 = 18 cm²
- Area covered = 120 − 18 = 102 cm²
Two identical squares of side 8 cm overlap. Together they cover 110 cm². What is the area of the shared part?
Primary 5 area of triangle questions, worked step by stepMark the base and its height on each figure first, then open the hint or the working.
In triangle JKL, KL = 18 cm. JM is drawn from J to meet KL at a right angle, and JM = 7 cm. JK = 9 cm. Find the area of triangle JKL.
- Area of triangle = 1/2 × base × height
- Base = KL = 18 cm, height = JM = 7 cm
- Area of triangle JKL = 1/2 × 18 × 7 = 63 cm²
In triangle DEF, EF = 9 cm. FE is extended to G, and DG meets it at a right angle. DG = 10 cm and EG = 4 cm. Find the area of triangle DEF.
- Base = EF = 9 cm (EG is outside the triangle)
- Height = DG = 10 cm
- Area of triangle DEF = 1/2 × 9 × 10 = 45 cm²
PQRS is a rectangular card with PQ = 20 cm and QR = 12 cm. T is a point on PQ such that TQ = 13 cm. Triangle PTS is cut off. Find the area of the card left.
- PT = 20 − 13 = 7 cm
- Area of card = 20 × 12 = 240 cm²
- Area of triangle PTS = 1/2 × 7 × 12 = 42 cm²
- Area left = 240 − 42 = 198 cm²
ABCD is a rectangle with AB = 24 cm and BC = 10 cm. P and Q are points on AB such that AP = 5 cm and QB = 7 cm. R is a point on DC. Find the area of triangle PQR.
- PQ = 24 − 5 − 7 = 12 cm
- Height = BC = 10 cm
- Area of triangle PQR = 1/2 × 12 × 10 = 60 cm²
Two identical right-angled triangles, each with a base of 12 cm and a height of 10 cm, overlap. The parts that are not shared have a total area of 84 cm². Find the area of the shared part.
- Area of 1 triangle = 1/2 × 12 × 10 = 60 cm²
- Area of 2 triangles = 60 × 2 = 120 cm²
- 2 shared parts = 120 − 84 = 36 cm²
- Shared part = 36 ÷ 2 = 18 cm²
Step 6
Check yourself
Five triangle questions. Nothing is saved, and each reply points to the question type to practise.
1. In triangle RST, SU is drawn from S to meet RT at a right angle. RT is the base. Which line is the height?
2. A triangle has a base of 16 cm and a height of 5 cm. What is its area?
3. In triangle ABC, BC = 8 cm. CB is extended to D, and AD meets it at a right angle. AD = 6 cm and AB = 10 cm. What is the area of triangle ABC?
4. ABCD is a rectangle with AB = 22 cm and BC = 6 cm. E is on DC. What is the area of triangle ABE?
5. Two identical squares of side 7 cm overlap in a square of side 2 cm. What area do they cover?
Using this guide at home. Before each figure moves, ask your child to point at the base and then at the height that goes with it. Once your child can do that every time, the rest of the chapter is mostly careful working on the right lengths.
When checking homework, look for the rule written as area of triangle = 1/2 × base × height before any numbers, and for a missing length worked out on its own line. If an answer looks too big, ask whether a sloping side was used as the height, or whether the half was left out.
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P5 Area of Triangle lessons and practice
5 lesson videos and 45 questions across five subtopics, from Basic to Challenge, each with a worked solution.
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