How to Find the Area of a Triangle: Formula, Examples & Practice

To find the area of a triangle, use the formula A = ½ × base × height. The height must be perpendicular (90°) to the base — not the slanted side. Example: a triangle with a base of 8 cm and a height of 6 cm has an area of ½ × 8 × 6 = 24 cm². This formula works for every type of triangle: right-angled, isosceles, equilateral, and scalene.

What Is the Area of a Triangle?

The area of a triangle is the measure of the region enclosed inside the triangle. The concept of the area of plane shapes has been used since ancient Egypt and ancient Greece — Archimedes developed systematic methods for computing the area of plane figures, including triangles, around the 3rd century BC. A triangle is a plane shape with three sides and three angles whose sum is always 180°.

There are several types of triangles: right-angled (one 90° angle), equilateral (all three sides equal), and scalene. The area formula works for every type of triangle.

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The Area of a Triangle Formula

Written as: A = ½ × base × height, or A = (base × height) ÷ 2

Important note: The height of the triangle must be perpendicular (90°) to the base. The height can sit inside the triangle (acute) or outside the triangle (obtuse).

💡 Tip to Remember the Formula: Picture a triangle as "half" of a rectangle or parallelogram. If you cut a rectangle along its diagonal, you get two identical triangles.

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How to Find the Area of a Triangle: Worked Examples

Example 1: Area of a Right Triangle

A right triangle has a base of 8 cm and a height of 6 cm. Find its area.

Step 1: Identify: base = 8 cm, height = 6 cm

Step 2: Substitute into the formula

Answer: Area of the triangle = 24 cm²

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Example 2: Finding the Base from the Area

A triangle has an area of 30 cm² and a height of 10 cm. What is the length of its base?

Step 1: Use the formula A = ½ × base × height and substitute the known values

Answer: Length of the base = 6 cm

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Example 3: Word Problem

Mr Budi in Bandung wants to paint the roof of his house, which is shaped like an isosceles triangle with a base of 10 m and a height of 4 m. What is the area of the roof that needs painting?

Step 1: base = 10 m, height = 4 m

Answer: Area of the roof = 20 m²

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Common Mistakes When Finding the Area of a Triangle

Mistake 1: Using the slanted side as the height The height of a triangle must be perpendicular (90°) to the base — not the slanted side. In a right triangle with sides 3 cm, 4 cm, and 5 cm (hypotenuse), the height is 3 cm or 4 cm (the perpendicular sides), not 5 cm. Using 5 cm as the height gives the wrong area.

Mistake 2: Forgetting to divide by two The area formula for a triangle is ½ × base × height. Many pupils calculate base × height without dividing by two. Remember: a triangle is half a parallelogram, so the result is always divided by 2.

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Area of a Triangle Table

💡 Quick Tip: If both the base and the height are even, divide one of them by 2 before multiplying. Example: base=12, height=8 → A = 6 × 8 = 48 cm² (easier than 12×8÷2).

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Practice Problems: Finding the Area of a Triangle

Problem 1: ⭐ A triangle has a base of 12 cm and a height of 7 cm. Find its area.

Problem 2: ⭐⭐ A triangle has an area of 45 cm² and a base of 9 cm. What is its height?

Problem 3: ⭐⭐⭐ A triangular garden in Surabaya has a base of 20 m and a height of 15 m. What is its area?

Answer Key:

1. A = ½ × 12 × 7 = 42 cm²
2. h = (45 × 2) ÷ 9 = 10 cm
3. A = ½ × 20 × 15 = 150 m²

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Summary

1. The area of a triangle is the region inside the triangle, computed with the formula A = ½ × base × height.
2. The height of the triangle must be perpendicular (90°) to the base — not the slanted side.
3. The formula works for every type of triangle: right-angled, isosceles, equilateral, and scalene.
4. To find the base or the height from a known area, use: base = (2 × A) ÷ height.
5. Area units are always squared: cm², m², etc. — don't forget to write the correct units.

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Also read: How to Calculate the Circumference of a Circle and How to Calculate LCM and GCF.