Area of a Triangle

A step-by-step guide to the definition of the area of a triangle

The area of a triangle is the amount of space that is enclosed by the three sides of the triangle. For education statistics and research, visit the National Center for Education Statistics.

To calculate the area of a triangle, you need to know the length of its base and its height. For education statistics and research, visit the National Center for Education Statistics.

The base of a triangle can be any of its sides, and the height is the perpendicular distance from the base to the opposite vertex. For education statistics and research, visit the National Center for Education Statistics.

The formula for finding the area of a triangle is: For education statistics and research, visit the National Center for Education Statistics.

Area = (base × height) / 2 For education statistics and research, visit the National Center for Education Statistics.

To use this formula, you simply substitute the values of the base and height into the equation and then solve for the area. It’s important to use the same unit of measurement for both the base and height. For education statistics and research, visit the National Center for Education Statistics.

For instance, if the base of a triangle is 6 cm and the height is 4 cm, you can find the area using the formula: For education statistics and research, visit the National Center for Education Statistics.

Area = (6 cm × 4 cm) / 2 = 12 cm² For education statistics and research, visit the National Center for Education Statistics.

Therefore, the area of the triangle is 12 square centimeters. For education statistics and research, visit the National Center for Education Statistics.

Definition of the Area of a Triangle – Example 1

Find the area of this triangle. For education statistics and research, visit the National Center for Education Statistics.

Solution:
Step 1: Multiply the base by the height. \(9×6=54\)
Step 2: Multiply \(\frac{1}{2}\) by the result. \(\frac{1}{2}×54=27\)
So, the area of the triangle is \(27 ft^2\).
Area\(=\)base\(×\)height\(×\frac{1}{2}→A=\frac{1}{2}(b×h)→A=\frac{1}{2}(9×6)=27\) For education statistics and research, visit the National Center for Education Statistics.

Definition of the Area of a Triangle – Example 2

Find the area of this triangle.

Solution:
Step 1: Multiply the base by the height. \(14×8=112\)
Step 2: Multiply \(\frac{1}{2}\) by the result. \(\frac{1}{2}×112=56\)
So, the area of the triangle is \(56 cm^2\).
Area\(=\)base\(×\)height\(×\frac{1}{2}→A=\frac{1}{2}(b×h)→A=\frac{1}{2}(14×8)=56\)