Triangle Area Calculator (Base and Height or Heron's Formula)
Pick what you know. With base and height, fill in the first two boxes. With three sides, fill in all three; the third box is ignored for base and height.
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Formula
- Base and height:
area = base × height ÷ 2 - Three sides (Heron's formula):
s = (a + b + c) ÷ 2, thenarea = √(s × (s − a) × (s − b) × (s − c))
Worked example
Base 10 and height 6: 10 × 6 ÷ 2 = 30.
Sides 13, 14 and 15: s = 21, so area = √(21 × 8 × 7 × 6) = √7056 = 84.
Frequently asked questions
What is the formula for the area of a triangle?
Half the base times the height. A triangle with base 10 and height 6 has area 10 × 6 ÷ 2 = 30.
How do I find the area when I only know the three sides?
Use Heron's formula: with s = (a + b + c) ÷ 2, the area is √(s(s−a)(s−b)(s−c)). For sides 13, 14 and 15, s = 21 and the area is √7056 = 84.
Why does the calculator say my sides are out of range?
Three lengths only form a triangle if each side is shorter than the sum of the other two. Sides 1, 2 and 10 cannot close up, and 1, 2 and 3 would be flat.
Does the height have to be a side of the triangle?
No. The height is the straight-line distance from the base to the opposite corner, at a right angle to the base, so it often lies inside the triangle rather than along a side.