Formula for the Area of a Triangle
The area of a triangle equals one-half times the base times the height, written as A = (1/2)bh or A = bh/2. Both forms give identical results. A right triangle with base 5 m and height 8 m has area (1/2)(5)(8) = 20 square meters. A triangular sign with base 40 cm and height 25 cm has area (40 times 25)/2 = 500 square cm. This formula is a core skill in 6th grade geometry covered in Reveal Math, Course 1, Module 8, and derives from the fact that a triangle is exactly half of a parallelogram.
Key Concepts
Property Since a triangle is half of a parallelogram, its area is one half of the base times the height. You can write this formula in two different, equally correct ways: $$A = \frac{1}{2}bh$$ or $$A = \frac{bh}{2}$$.
Session 2. Formula for the Area of a Triangle.
Property Examples A right triangle has a base of 5 m and a height of 8 m. Its area is 1/2 x 5 x 8 = 20 square meters. A triangular sign has a base of 40 cm and a height of 25 cm. Using the alternative notation: (40 x 25) / 2 = 1000 / 2 = 500 square cm. An obtuse triangle has a base of 10 inches and a height of 6 inches. The area is 1/2 x 10 x 6 = 30 square inches.
Common Questions
What is the formula for the area of a triangle?
The formula is A = (1/2) times b times h, where b is the base and h is the perpendicular height. You can also write it as A = bh divided by 2 — both forms give the same answer.
How do I calculate the area of a triangle step by step?
Multiply the base by the perpendicular height, then divide by 2. For a triangle with base 10 cm and height 6 cm: (10 times 6) divided by 2 = 30 square cm.
Why does the triangle area formula divide by 2?
A triangle is exactly half of a parallelogram with the same base and height. The parallelogram area is bh, so the triangle area is (1/2)bh.
Does the triangle area formula work for all types of triangles?
Yes, the formula A = (1/2)bh works for right triangles, acute triangles, and obtuse triangles, as long as you use the perpendicular height and not the slanted side.
What is the most common mistake when finding triangle area?
Forgetting to multiply by 1/2 or divide by 2. If you just multiply base times height without dividing by 2, you calculate the area of the full parallelogram, which is double the triangle area.
When do 6th graders learn the triangle area formula?
The triangle area formula is taught in 6th grade geometry in Module 8 of Reveal Math, Course 1.