Question
A triangle has a base of 10 cm and a height of 6 cm. Find its area.
Solution — Step by Step
The area of any triangle is:
Why half? Because a triangle is exactly half of a parallelogram with the same base and height. This is the geometric reason behind the formula — not just a rule to memorise.
From the question:
- Base = 10 cm
- Height = 6 cm
The height must be perpendicular to the base — this is the key condition. It doesn’t matter if the triangle is acute, right-angled, or obtuse; as long as the perpendicular height is 6 cm, the formula applies directly.
Area = 30 cm²
Why This Works
Every triangle can be paired with a parallelogram that shares the same base and height. The area of that parallelogram is simply base × height. The triangle occupies exactly half of it — you can verify this by cutting a paper parallelogram diagonally.
This is why the formula works for all triangles — scalene, isosceles, equilateral, right-angled. The shape of the sides doesn’t change the formula; only the base and the perpendicular height matter.
In CBSE Class 7 and 8 exams, a common shortcut: if the base and height are both even numbers, just multiply them and divide by 2 mentally. Here, 10 × 6 = 60, halve it → 30. Done in one step.
Alternative Method
We can also work backwards to verify. If the area is 30 cm², then:
This reverse approach is useful when exam questions give you the area and ask for the base or height. The rearranged formulas are:
Memorise both forms — NCERT exercises regularly ask for missing dimensions.
Common Mistake
Forgetting the ½ factor. Many students write Area = base × height = 60 cm² and move on. This is the formula for a parallelogram, not a triangle. Always check: if your answer looks “too big” compared to the given dimensions, you’ve likely missed the half. In this question, 60 cm² is wrong — 30 cm² is correct.
Another trap: using the slant side as the height. The height is always the perpendicular distance from the base to the opposite vertex. If the question gives a slanted side length instead of the perpendicular height, you cannot directly use it in the formula without further calculation.