Primary 5 · Mathematics

P5 area of triangle

The formula is the easy part: half times base times height. The marks are lost on one word, height, because the length the eye reaches for is usually the wrong one.

Level
P5
Usually taught
Term 2
Covers
1 concept

What changes at P5

At Primary 5, the area of a triangle arrives with a formula that looks simple: half times base times height. Your child multiplies two lengths and halves the result. The multiplying is not the hard part.

The difficulty is one word: height. The height is the distance from the base to the opposite corner, measured at a right angle, and it is often not one of the sloping sides the triangle happens to be drawn with.

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 arithmetics are clean. The only question is which length is the height, and only the right-angle marker settles it. That is why it is so hard to catch over a shoulder.

6 cm4 cm
The height meets the base at a right angle, inside the triangle.
6 cm4 cm
Tilt it and the height falls outside. Still a right angle to the base.

The same question, worked properly

  1. Pick the base and its height

    base = 6 cm

    Any of the three sides can be the base. Once you pick one, the height is the perpendicular distance from it to the opposite corner, not the sloping side.

  2. Read the height, not the slant

    height = 4 cm

    This is the step that fails. The right-angle marker points to the height. The 5 cm sloping side sits right beside it and is the number most working reaches for without checking.

  3. Multiply, then halve

    area = 12×6×4\frac{1}{2} \times 6 \times 4 = 12 cm²

    Half of six times four. The half is what makes it a triangle and not a rectangle.

  4. When the height is outside

    area = 12×base×height\frac{1}{2} \times \text{base} \times \text{height}

    On a tilted or obtuse triangle the height lands outside the shape, down onto the base extended. The rule does not change: it is still the perpendicular height.

How can you tell it has clicked?

You do not need to work out the area to check this. Point at the 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.

One thing to try 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. That right angle is the one thing to look for every time.

What your child will meet in this topic

  • Triangle Area

Most Singapore schools introduce this in Term 2, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.

What it leads to

Base times height, halved, runs straight into composite figures: an L-shape split into rectangles and triangles, or a triangle sitting inside a rectangle. Each piece needs its own base and its matching height.

A child who always finds the perpendicular height handles those. A child who grabs a printed side gets most of a composite question right and still loses the triangle's marks.

The same topic in other years

It comes back each year and gets harder, so it helps to see what came before and what is coming.

More in Primary 5

Other topics in the same year, so you can see what sits either side of this one.

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.

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