The figure shows triangle LMN. MN is 26 centimetres. LP is 15 centimetres and meets MN at a right angle. Find the area of triangle LMN.
The area of triangle LMN is 195 cm².
Ans: 195 cm²
Example 1 of 2
The figure shows triangle PQR. QR is 11 centimetres. RQ is extended to S. PS is 12 centimetres and meets RS at a right angle. QS is 5 centimetres. PR is 20 centimetres. Find the area of triangle PQR.
Triangle PQR has an area of 66 cm².
Ans: 66 cm²
Example 2 of 2
The figure shows triangle TUV. UV is 15 centimetres and is taken as the base. TW is 8 centimetres and meets UV at a right angle. TU is 10 centimetres. Find the area of triangle TUV.
Triangle TUV has an area of 60 cm².
Ans: 60 cm²
How to solve it
Choose the base, then find the height: the line from the opposite corner that meets the base at a right angle.
Write the rule: area is one half times base times perpendicular height. Two equal triangles make a rectangle, so one triangle is half.
Put in the numbers: the base is 26 centimetres and the height is 15 centimetres, so the area is half of 26 times 15.
Cancel the 2 with 26 first. That leaves 13 times 15, which is 195 square centimetres.
If the height falls outside the triangle, extend the base and use the line that meets it at a right angle.
Inside or outside, and whichever way the base is drawn: choose the perpendicular height, then use half times base times height.
Practice questions with worked solutions
Question 1 is free to try. The other 5 open in the free trial, each with its full working.
How do you work out P5 area of a triangle questions?
This page teaches the area of a triangle as half of a rectangle with the same base and height, from the Primary 5 Area and Volume strand.
What your child learns here
This page teaches the area of a triangle as half of a rectangle with the same base and height, from the Primary 5 Area and Volume strand. It includes triangles drawn on a slant and obtuse triangles, where the height falls outside.
Area of a triangle = one half × base × height, written in square units such as cm².
The height used must be perpendicular to the base it is paired with.
In an obtuse triangle the height can meet the base extended, outside the triangle, while the base itself stays the side of the triangle.
Lengths printed on a figure that are neither the base nor its height are not needed for the area.
The same idea leads on to composite figures made up of rectangles, squares and triangles.
Does the answer make sense?
Your child's triangle area must be less than its base times its height, because the triangle is exactly half of the rectangle with that base and height. An answer as big as base times height has lost the half, and an answer in cm rather than cm² has lost its square unit.
How to practise these questions
The Basic questions train your child to pair each base with its own perpendicular height and to remember the half, even when the figure is turned or obtuse. Intermediate questions add bases split into two printed pieces and right-angled triangles resting on their longest side. In the Challenge question the base is never printed, so it has to be found from the perimeter before any area work begins. If your child stalls, watch the solution film for that triangle, then return to it later from Revision. The multiple-choice questions compare the areas of triangles that share a base or a height at Basic, and at Intermediate a triangle split by a point on one side or triangles given their bases and heights; each has written working and no film.
Questions parents ask
What is the formula for the area of a triangle in Primary 5? Area of triangle = one half × base × height. The height must be perpendicular to the base chosen, and the answer is written in square units.
Why is the area of a triangle half of base times height? Two copies of the same triangle fit together to make a shape with the same base and height as a rectangle. The lesson on this page shows two equal triangles making a rectangle, so one triangle is half of it.
Is area of composite figures part of this chapter? Yes. The Primary 5 syllabus includes finding the area of composite figures made up of rectangles, squares and triangles, which follows on from the area of a triangle.
