Example 1: Find the area of an acute triangle with a base of 15 inches and a height of 4 inches.

Solution:

= **·** (15 in) **·** (4 in)

** = ****·** (60 in^{2})

= 30 in^{2}

Example 2: Find the area of a right triangle with a base of 6 centimeters and a height of 9 centimeters.

Solution:

= **·** (6 cm) **·** (9 cm)

** = ****·** (54 cm^{2})

= 27 cm^{2}

Example 3: Find the area of an obtuse triangle with a base of 5 inches and a height of 8 inches.

Solution:

= **·** (5 in) **·** (8 in)

** = ****·** (40 in^{2})

= 20 in^{2}

Example 4: The area of a triangle shaped mat is 18 square feet and the base is 3 feet. Find the height. *(Note: The triangle in the illustration to the right is NOT drawn to scale.)*

Solution:

In this example, we are given the area of a triangle and one dimension, and we are asked to work backwards to find the other dimension.

18 ft^{2} = \B7 (3 ft) **· **h

Multiplying both sides of the equation by 2, we get:

36 ft^{2} = (3 ft) **· **h

Dividing both sides of the equation by 3 ft, we get:

12 ft = h

Commuting this equation, we get:

h = 12 ft

Summary: Given the base and the height of a triangle, we can find the area. Given the area and either the base or the height of a triangle, we can find the other dimension. The formula for area of a triangle is:

or where b is the base and h is the height.