The figure shows triangle FGH. Two lines are drawn in dashes. FJ, which meets GH at a right angle, and HK, which meets FG at a right angle. FG is taken as the base of the triangle. Which line is the height of triangle FGH?
So HK is the height of triangle FGH.
Ans: HK
Example 1
The figure shows triangle STU. UT is extended to V, and SV is drawn to meet it at a right angle. TW is drawn from T to meet SU at a right angle. TU is taken as the base of the triangle. Which line is the height of triangle STU?
So SV is the height of triangle STU.
Ans: SV
How to solve it
Choose the base: the side the question gives. For triangle FGH that is FG.
Find the corner the base does not touch. The height starts there, so it starts at H.
From that corner, take the dashed line that meets the base at a right angle. HK meets FG, so HK is the height.
If the corner leans back over the base, extend the base. The height lands on the extended line, outside the triangle.
Choose a different base and the height is a different line. FJ is the height when GH is the base.
The base is a choice. The height is whatever is perpendicular to the base you chose.
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 answer P5 base and height of a triangle questions?
Before any area is worked out, a child has to say which line is the height for a given base.
What your child learns here
Before any area is worked out, a child has to say which line is the height for a given base. This page teaches that idea from the Primary 5 Area and Volume strand, on triangles turned every way round.
Any side of a triangle can be chosen as the base.
The height for that base is the line from the opposite vertex that meets the base, or the base extended, at a right angle.
A triangle has three bases and three heights, and each height belongs to one base only.
In a right-angled triangle, the two sides that form the right angle are a base and height for each other.
When the height falls outside the triangle, the base is extended with a dotted line to meet it.
Does the answer make sense?
The height your child names must start at the one vertex the chosen base does not touch, and meet that base, or the base extended, in a square corner. When an area is asked and two base-and-height pairs are marked, both pairs must give the same area.
How to practise these questions
Basic practice asks for the height of a plain right-angled triangle tilted on the page, with nothing dashed to help. Intermediate questions crowd the figure with several perpendiculars, or a foot outside the triangle, so each height must be matched to its own base. At Challenge level the heights carry lengths and the area is asked, so choosing the matching base and height decides the answer. When a figure will not make sense, watch the solution film for that question and try it again later from Revision. Its multiple-choice questions name a base and ask which line is the matching height, or name a height and ask for its base, with Intermediate figures that carry two perpendiculars or two triangles on one base; the working is written, not filmed.
Questions parents ask
Can the height of a triangle be outside the triangle? Yes. In an obtuse triangle, the height for some bases meets the base extended, outside the triangle. The base itself does not change; it is only drawn longer to show where the height lands.
Does every triangle have three heights? Yes. Each of the three sides can be the base, and each base has its own height from the opposite vertex.
Where does base and height come in the syllabus? It is the first outcome of Area of Triangle in the Primary 5 syllabus: concepts of base and height of a triangle. It comes before working out the area.
