Lesson 3: Area of Triangles

Property

A triangle is exactly half of a parallelogram with the same base and height. To find its area, choose any side of the triangle as its base (length $b$), and let $h$ be the perpendicular distance from the base to its opposing vertex.
The formula is:

Examples

• A right triangle has legs (base and height) of 5 m and 8 m. Its area is $\frac{1}{2} \times 5 \times 8 = 20$ square meters.
• A triangular sign has a base of 40 cm and a height of 25 cm. Its area is $\frac{1}{2} \times 40 \times 25 = 500$ square cm.
• An obtuse triangle has a base of 10 inches and its corresponding height is 6 inches. The area is $\frac{1}{2} \times 10 \times 6 = 30$ square inches.

Explanation

Any triangle is exactly half of a parallelogram! If you clone a triangle, flip it, and join it to the original, you create a parallelogram. That's why the triangle's area formula is simply one-half of the base times the height.

Property

The area of a right triangle equals half the product of its two legs:

Examples

Property

If you know the area of a triangle and one of its dimensions (base or height), you can rearrange the area formula to solve for the missing dimension.

Given the area formula $A = \frac{1}{2}bh$:

• To find the height:
  $$h = \frac{2A}{b}$$
• To find the base:
  $$b = \frac{2A}{h}$$