Area of Triangles

Study Sheet

Area of Triangles

Half of a rectangle

Where the Half Comes From

Concept
The Big Idea
106

Any triangle is exactly half of a rectangle with the same base and height — that is where the 12\dfrac{1}{2} in the formula comes from.

Tip
The formula

Area =12bh= \dfrac{1}{2}bh, where hh is measured perpendicular to the base, not along a slanted side.

Example
Base 10, height 6

Area =12(10)(6)=30= \dfrac{1}{2}(10)(6) = 30 square units.

In Plain Terms & More Examples

Concept
In plain terms

A triangle is half a rectangle with the same base and height, so its area is 12×base×height\tfrac{1}{2} \times \text{base} \times \text{height}.

Example
Base 8, height 5

Area =12(8)(5)=20= \dfrac{1}{2}(8)(5) = 20 square units.

Example
Base 12, height 3

Area =12(12)(3)=18= \dfrac{1}{2}(12)(3) = 18 square units.