Triangle Area: Step-by-Step Guide
The area of a triangle is half of the base times the height. The height is the straight-up distance from the base to the opposite corner. It makes a right angle with the base.
Math Racer skill guide · Middle School · Grades 6-8
How to solve it, step by step
- Find the base and the height. Pick one side to be the base. The height is the distance from the opposite corner straight down to the base, making a right angle.\[b = \text{base},\; h = \text{perpendicular height}\]
- Write the formula. The area of a triangle is one-half times base times height.\[A = \tfrac{1}{2} b h\]
- Put in the numbers and work it out. Replace b and h with the numbers. Multiply them, then take half.\[A = \tfrac{1}{2}(b)(h)\]
- Write the units. Area is always in square units, like square inches.\[A = \text{value}\;\text{units}^2\]
Worked example
A triangle has a base of 10 inches and a perpendicular height of 6 inches. Find its area.
Step 1: The base is 10 inches and the height is 6 inches.
Step 2: The formula is area = (1/2) x base x height.
Step 3: Put in the numbers: area = (1/2) x 10 x 6.
Step 4: Multiply the base and height: 10 x 6 = 60.
Step 5: Take half: 60 / 2 = 30.
Step 6: Add the units: the area is 30 square inches.
Check: Two of these triangles fit together to make a 10 by 6 rectangle with area 60. One triangle is half of that, which is 30.
Tips and common mistakes
- The height must make a right angle with the base. It is not the slanted side of the triangle.
- In a right triangle, the two sides that meet at the right angle can be the base and the height.
- In some triangles, the height falls outside the triangle. Extend the base line to see it.
- Do not forget the 1/2. Without it, you get the area of a rectangle or parallelogram, which is twice as big.
- Make sure the base and height are in the same unit before you multiply.
- Draw the triangle and mark where the height goes. This keeps you from using the wrong length.