Primary 5 maths · Measurement & time · About 12 minutes
Identify a triangle base and perpendicular height
Find the right-angle relationship before using a dimension. For a composite surface, keep the pieces separate.
Start the interactive lesson →Open practice activity
What you will learn
- Identify a triangle base and perpendicular height
Models used: number sentences, stories, diagrams.
Before you start
Which height belongs to this base?
Choose the bottom edge as our base. It is 6 units long.
Base = 6 units. Perpendicular height = 4 units. The little square marks a right angle.
Choose the bottom edge as our base. It is 6 units long.
A height belongs to a particular base. Choose the base before looking for its height.
Base = 6 units. Perpendicular height = 4 units. The little square marks a right angle.
Look at the little square in the corner. The upright side meets the base at a right angle.
The height is the straight distance from the opposite vertex to the base line, measured at a right angle.
Base = 6 units. Perpendicular height = 4 units. The little square marks a right angle.
For this base, the height is 4 units. The sloping edge is not the matching height.
The height tells us how far the triangle reaches away from its base.
Can we use whichever side looks longest as the height?
No. Check the right angle. The height must be perpendicular to the chosen base.
What did the picture help us see?
For this base, the height is 4 units. The sloping edge is not the matching height.
Worked example: A new example, together
Which measurement is the height for the horizontal base in this triangle?
Base = 1 units. Perpendicular height = 1 units. The little square marks a right angle.
Find the right-angle relationship before using a dimension. For a composite surface, keep the pieces separate.
Base and height meet at a right angle, matching a surrounding rectangle.
Base = 1 units. Perpendicular height = 1 units. The little square marks a right angle.
Choose the stated base.
Which measurement is the height for the horizontal base in this triangle?
The perpendicular distance from the opposite vertex to the base line
Base = 1 units. Perpendicular height = 1 units. The little square marks a right angle.
Choose the stated base.
Base = 1 units. Perpendicular height = 1 units. The little square marks a right angle.
Draw or locate a line perpendicular to its line from the opposite vertex.
Base = 1 units. Perpendicular height = 1 units. The little square marks a right angle.
That distance at a right angle is the matching height.
Base = 1 units. Perpendicular height = 1 units. The little square marks a right angle.
Check the result against the question we started with.
The marked height meets the base line at 90°.
We found The perpendicular distance from the opposite vertex to the base line. Base and height meet at a right angle, matching a surrounding rectangle.
Common mistakes to discuss
- Using a slanting side as the height. The height meets the base at a right angle. The sloping side is longer and gives too large an area.
Check your understanding
- Identify a triangle base and perpendicular height
- connect triangle area to a matching base and perpendicular height
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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