How to Find the Area of a Triangle
- Identify the base and height of the triangle.
- Evaluate the area of a triangle formula with the base and height of the triangle.
- Make sure the answer is labeled with the correct units.
Examples
Right Triangle
What is the base of the triangle?
The base of the triangle is 4 cm.
What is the height of the triangle?
The height of the triangle must be perpendicular to the base, so the height of this triangle is 3 cm.
What is the evaluated formula for the area of this triangle?
\[A=\frac{1}{2}(4\, cm)(3\, cm)\]
Four times three equals twelve.
\[A=\frac{1}{2}(12\, cm^2)\]
One half times twelve equals six.
\[A=6\, cm^2\]
What are the correct units for the area of this triangle?
The side lengths of the triangle were measured in centimeters, so the area of the triangle should be measured in square centimeters.
The area of this triangle is \(6\, cm^2\).
Acute Triangle
What is the base of the triangle?
The base of the triangle is 10 m.
What is the height of the triangle?
The height of the triangle must be perpendicular to the base, so the height of this triangle is 4 cm.
What is the evaluated formula for the area of this triangle?
\[A=\frac{1}{2}(10\, m)(4\, m)\]
Ten times four equals forty.
\[A=\frac{1}{2}(40\, m^2)\]
One half times forty equals twenty.
\[A=20\, cm^2\]
What are the correct units for the area of this triangle?
The side lengths of the triangle were measured in meters, so the area of the triangle should be measured in square meters.
The area of this triangle is \(20\, m^2\).
Obtuse Triangle
What is the base of the triangle?
The base of the triangle is 6 in.
What is the height of the triangle?
The height of the triangle must be perpendicular to the base and span the entire height of the triangle, so the height of this triangle is 5 in.
What is the evaluated formula for the area of this triangle?
\[A=\frac{1}{2}(6\, in)(5\, in)\]
Six times five equals thirty.
\[A=\frac{1}{2}(30\, in^2)\]
One half times thirty equals fifteen.
\[A=15\, in^2\]
What are the correct units for the area of this triangle?
The side lengths of the triangle were measured in inches, so the area of the triangle should be measured in square inches.
The area of this triangle is \(15\, in^2\).
Choosing the Base
Technically, the base of the triangle can be any of the three sides of the triangle. The height of the triangle has to be perpendicular to the base.
In most diagrams, the base of the triangle will be drawn across the bottom of the diagram.
However, some diagrams may be rotated and the side of the triangle that has a corresponding height may be slanted, vertical, or drawn across the top of the diagram.
In this diagram, the base of the triangle is 8 meters because that is the only side of the triangle that has a perpendicular height (4 meters).
