Area⏱ 4 min read

Area of a Triangle

A = ½ × b × h

What is the Area of a Triangle?

The area of a triangle equals half the base times the height, and this holds for every triangle — right, acute, or obtuse. The key detail is that h must be the perpendicular height, measured straight up from the base to the opposite vertex, not the length of one of the triangle's slanted sides.

The formula comes directly from a rectangle: any triangle is exactly half of the rectangle (or parallelogram) that shares the same base and height, which is why the area works out to exactly half of b × h.

What Each Variable Means

AreaThe two-dimensional space enclosed by the triangle.

BaseThe length of any one side, chosen as the base.

HeightThe perpendicular distance from the base to the opposite vertex — not the length of a slanted side.

When to Use It

Finding the area of any triangle when its base and perpendicular height are known
As a building block for the areas of more complex polygons, which can often be split into triangles
Estimating material or land area for triangular regions

Step-by-Step Example

Problem: A triangle has a base of 8 cm and a height of 5 cm. Find its area.

Identify the base and height

Both are given directly.

b = 8 cm, h = 5 cm

Apply the formula

Multiply base by height, then halve the result.

A = ½ × 8 × 5 = ½ × 40

✓

Answer: A = 20 cm²

Interactive Calculator

b (base)h (height)

Result will appear here

Common Mistakes

Mistake: Using a slanted side's length instead of the perpendicular height.
Fix: h must be measured perpendicular to the base — straight up to the opposite vertex, not along one of the triangle's other sides.
Mistake: Forgetting the ½ factor.
Fix: A = ½bh, not simply bh — dropping the ½ doubles the area, which is actually the area of the parallelogram the triangle is half of.

Practice Questions

A triangle has base 10 m and height 6 m. Find its area.
A triangle has an area of 24 cm² and a base of 8 cm. Find its height.
Hint: Rearrange A = ½bh to solve for h.

Frequently Asked Questions

Does it matter which side I choose as the base?

No — any side can serve as the base, as long as you measure the perpendicular height to that specific side's opposite vertex. The area comes out the same regardless of which side you pick.

Is there a formula for area when only the three sides are known?

Yes — Heron's formula computes area directly from the three side lengths without needing the height separately.