Primary 5 · Measurement & Geometry

P5 area of triangle

Area of a triangle is half of base times height. The formula is the easy part. In P5, your child learns which length is the height, finds the area of any triangle, and works out composite figures made of rectangles, squares and triangles.

Taught in
Term 2
Syllabus
3 skills
Usual slip
Uses the slant side

An acute triangle with a base of 6 cm and a perpendicular height of 4 cm

What your child learns in P5 area of triangle

Three skills, each with what it looks like on a worksheet.

Follows the latest (2026) MOE syllabus
See the syllabus wording
  • concepts of base and height of a triangle
  • area of triangle
  • finding the area of composite figures made up of rectangles, squares and triangles

Base and perpendicular height

Any side can be the base. The height is the line from the opposite corner that meets the base at a right angle. It can fall inside the triangle, along a side, or outside it.

Height inside
Height outside

Area of a triangle

Area = half × base × height. A triangle is half of the rectangle with the same base and height, which is why the formula halves. A base of 6 cm and a height of 4 cm give 12 cm².

Half of the rectangle

Composite figures

Split the figure into rectangles, squares and triangles, find each area, then add them. Or take a triangle away from the rectangle that holds it.

6 cm4 cm3 cm
Rectangle + triangle

Key facts and formulas

Term 2
  • 12 cm7 cm
    Area of a triangle12×base×height\tfrac{1}{2} \times \text{base} \times \text{height}Example12×12×7=\frac{1}{2} \times 12 \times 7 = 42 cm242\,\text{cm}^{2}
  • 4 cm6 cm
    The height can be outsideIt is always at right angles to the base.12×4×6=\frac{1}{2} \times 4 \times 6 = 12 cm212\,\text{cm}^{2}
  • 10 cm6 cm
    Half of its rectangleSame base and height as the rectangle: half its area.12×10×6=\frac{1}{2} \times 10 \times 6 = 30 cm230\,\text{cm}^{2}
  • 3 cm4 cm8 cm
    Composite figuresSplit into rectangles, squares and triangles. Add, or take away.8×4+12×8×3=8 \times 4 + \frac{1}{2} \times 8 \times 3 = 44 cm244\,\text{cm}^{2}

Words to know

Base
The side you measure from. Any side of a triangle can be the base.
Perpendicular height
The distance from the base to the opposite corner, measured at a right angle.
Right angle
A 90° corner, shown by a small square where two lines meet.
Opposite vertex
The corner of the triangle facing the base you chose.

The sentence that costs the mark

A triangle has a base of 6 cm and a sloping side of 5 cm. Its perpendicular height, meeting the base at a right angle, is 4 cm. Find its area.

What the working usually does

12×6×\frac{1}{2} \times 6 \times5 cm=15 cm²

Reaches for the 5 cm sloping side, the length printed right next to the base. It is a real side of the triangle, so the answer looks reasonable.

What the question asked

12×6×\frac{1}{2} \times 6 \times4 cm=12 cm²

Uses the 4 cm perpendicular height, the one that meets the base at a right angle. That right angle is the whole test.

Both lines are half times 6 times a length, and both are worked correctly. The only question is which length is the height, and only the right-angle marker settles it.

The same P5 area of triangle question, worked properly

Lah works through it the way she does every question in StudyLah: one step at a time, marking the picture as she goes.

Find the area of the shaded triangle PQS.

8 cm4 cm9 cm15 cmPQRS
Step 1 of 5▌
  1. To find a triangle's area, use half of the base times the height. Take PQ as the base, so the base = 8 cm.
  2. The height must meet the base at a right angle. That is RS = 9 cm, not the slanted side PS, which is 15 cm.
  3. The foot R is outside PQ, which is fine. The 4 cm from Q to R is not part of the base, so the base stays 8 cm.
  4. Area = 12\frac{1}{2} × 8 × 9 = 36 cm².
  5. So the shaded triangle is 36 cm².

Every question in StudyLah comes with a walkthrough like this one.

Try it free

Two quick P5 area of triangle questions

Try them together, then tap to check.

Question 1

In triangle WXY below, which line is the height when XY is the base?

AWXYZ
Show answer

AnswerWA. It starts at W, the corner opposite XY, and meets XY at a right angle. YZ is the height for base WX.

Question 2

Find the area of triangle PQR shown below.

6 cm5 cm10 cm3 cmPQR
Show answer

Answer15 cm². The base PR is 5 cm and the height is 6 cm, so the area is half of 5 × 6. PQ, 10 cm, is a slant side.

Helping at home

How to tell it has clicked

You do not need to work out the area to check this. Point at a triangle, ask your child to show you the height, then ask one thing: where is the right angle?

A child who understands puts a finger on the line that meets the base square-on, even when it falls outside the triangle. A child who points at a sloping side has found the exact gap the marks fall through.

Try this tonight

Draw any triangle and stand the corner of a book on its base. The edge of the book that rises straight up, at a right angle, is the height. The sloping side of the triangle never is.

Slide the book along and the height changes with the base you picked, but it always meets that base at a right angle.

Before and after P5 area of triangle

  1. Builds on

    Primary 4 Area and Perimeter

    Splits for area, traces for perimeter

  2. You are here

    Primary 5 Area of Triangle

    Halves base times perpendicular height

In the PSLE's hardest questions

More in Primary 5

Struggling with the working rather than the topic itself? How to help your child with problem sums

See how your child is doing on this topic

StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.

Try it free