8-2 Area of Triangles

Property

Two identical (congruent) triangles can always be joined together to form a parallelogram.

Therefore, the area of a single triangle is exactly half the area of a parallelogram that shares the same base and height.

Examples

• Right Triangles: Two identical right triangles can be joined along their longest side (the diagonal) to form a rectangle, which is a type of parallelogram.
• General Triangles: Take any triangle. If you make an exact copy, rotate it 180°, and join it to the original, the combined shape is a parallelogram. If that parallelogram has an area of 40 square cm, one triangle has an area of 20 square cm.

Property

Since a triangle is half of a parallelogram, its area is one-half of the base times the height. You can write this formula in two different, equally correct ways:

or

Session 2. Formula for the Area of a Triangle

Property

Examples

• A right triangle has a base of 5 m and a height of 8 m. Its area is 1/2 x 5 x 8 = 20 square meters.
• A triangular sign has a base of 40 cm and a height of 25 cm. Using the alternative notation: (40 x 25) / 2 = 1000 / 2 = 500 square cm.
• An obtuse triangle has a base of 10 inches and a height of 6 inches. The area is 1/2 x 10 x 6 = 30 square inches.