Area of a Triangle - Examples

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

Solution:

acute triangletriangle

a_0.gif = one_half.gif· (15 in) · (4 in)

a_0.gif = one_half.gif· (60 in2)

a_0.gif = 30 in2


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

right triangleSolution:

triangle

a_0.gif = one_half.gif· (6 cm) · (9 cm)

a_0.gif = one_half.gif· (54 cm2)

a_0.gif = 27 cm2


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

Solution:

obtuse triangletriangle

a_0.gif = one_half.gif· (5 in) · (8 in)

a_0.gif = one_half.gif· (40 in2)

a_0.gif = 20 in2


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.

right triangletriangle

18 ft2 = one_half.gif\B7 (3 ft) · h

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

36 ft2 = (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:

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

 

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