A triangle is a three-sided polygon with three vertices and three edges. The area of a triangle is the total space enclosed within its three sides, measured in square units such as square meters (m²), square feet (ft²), or square centimeters (cm²).
The most common method to calculate a triangle's area uses the base (any side of the triangle) and the height (the perpendicular distance from the base to the opposite vertex). This formula works for all types of triangles: equilateral, isosceles, scalene, and right triangles.
Calculating the area of a triangle using base and height is simple:
The height must be perpendicular (at a 90-degree angle) to the base for accurate results.
Or written mathematically:
Where:
Problem: Calculate the area of a triangle with base 10 cm and height 6 cm.
Solution:
Problem: A right triangle has legs of 8 inches and 15 inches. What is its area?
Solution: In a right triangle, the two legs can serve as base and height.
A triangle is essentially half of a rectangle or parallelogram with the same base and height. Imagine drawing a diagonal through a rectangle - you get two identical triangles, each with half the rectangle's area.
Yes! You can choose any of the three sides as the base. However, you must use the height that corresponds to that specific base - the perpendicular distance from that base to the opposite vertex.
If you know all three sides but not the height, you can use Heron's formula: A = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (a+b+c)/2.