How to Find the Area of a Triangle

Calculating the area of a triangle can be done in two popular ways: the base-height method and Heron's formula. Each method has its benefits.

Base-Height Method

• Easy to Use: This method is simple! If you know the base (that's the bottom of the triangle) and the height (the straight line from the base to the top), you can find the area. Just use this formula:

  $$A = \frac{1}{2} b h$$

  Here, ( A ) is the area, ( b ) is the base, and ( h ) is the height.

• Helps You See It: This method lets you look at the triangle more clearly. It’s especially helpful when you are working with graphs or drawing triangles.

Heron's Formula

• Works with Just the Sides: Heron's formula is great when you only have the lengths of all three sides of the triangle, which we can call ( a ), ( b ), and ( c ). To find the area, you use this formula:

  $$A = \sqrt{s(s-a)(s-b)(s-c)}$$

  where ( s ) is the semi-perimeter, or half of the triangle's total side lengths. You can find ( s ) by using this calculation:

  $$s = \frac{a + b + c}{2}$$

• No Height Needed: With Heron's formula, you don’t need to measure the height. This can be helpful because measuring the height can sometimes be hard, especially with unusual triangle shapes.

In Summary

Use the base-height method when you want an easy calculation and a clear picture of the triangle. Choose Heron's formula when you only have the lengths of the sides to work with!