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Triangle Area Calculator

A triangle is a fundamental three-sided polygon whose area equals exactly half the area of a rectangle with the same base and perpendicular height. Th

Mathematics
Formula & Methodology
Triangle Area = ½ × Base × Height = (b × h) ÷ 2

To compute the area of any triangle: 1. Measure the length of any side to serve as the base (b). 2. Measure the perpendicular height (h) dropped at a 90° right angle from the opposite vertex down to the base line. 3. Multiply the base by the height and divide by 2. This formula holds true for all triangles: acute, right, and obtuse.

Triangle Area

30

Overview

A triangle is a fundamental three-sided polygon whose area equals exactly half the area of a rectangle with the same base and perpendicular height. This free Triangle Area Calculator computes the exact square area for any triangle using the standard base-height method.

Calculating triangle area is essential in structural roof truss construction, surveying land acreage, triangular paving layout, and structural load analysis.

Worked Examples

Example 1: Standard Triangle (Base 10, Height 6)

Inputs: Base = 10, Height = 6

  1. Multiply base by height: 10 × 6 = 60.
  2. Divide by 2: 60 ÷ 2 = 30.
Final Answer: 30.00 sq units

Example 2: Right Triangle Legs (Base 8, Height 15)

Inputs: Base = 8, Height = 15

  1. Multiply: 8 × 15 = 120.
  2. Divide by 2: 120 ÷ 2 = 60.
  3. Hypotenuse check: √(8² + 15²) = 17.
Final Answer: 60.00 sq units

Example 3: Roof Truss Section (Base 24 ft, Height 8 ft)

Inputs: Base = 24, Height = 8

  1. Multiply: 24 × 8 = 192.
  2. Area: 192 ÷ 2 = 96 sq ft.
Final Answer: 96.00 sq ft

How to Use This Calculator

  1. Enter the base length in the first field.
  2. Enter the perpendicular vertical height in the second field.
  3. Click "Calculate" to determine the triangle area.
  4. Review the evaluated equation and right-triangle metrics below.
  5. Click "Reset" to test a new triangle.

Reference Table

Base (b)Height (h)CalculationArea Result
640.5 × 6 × 412.00
850.5 × 8 × 520.00
1060.5 × 10 × 630.00
1280.5 × 12 × 848.00
20150.5 × 20 × 15150.00

Frequently Asked Questions

What if I know all three side lengths instead of the height?
If you have side lengths a, b, and c without height, use our Triangle Calculator which computes area via Heron's formula: √[s(s-a)(s-b)(s-c)].
Must the height be one of the triangle's sides?
Only in a right triangle does the height equal one of the sides. In acute and obtuse triangles, height is an internal or external altitude line perpendicular to the base.
Why is the triangle area formula divided by 2?
Because any triangle can be duplicated and reflected to form a parallelogram of area b × h. The triangle is exactly half of that parallelogram.
Does the orientation of the triangle change its area?
No. Any of the three sides can be selected as the base, provided the corresponding perpendicular height to the opposite vertex is used.
Can this calculate equilateral triangle area?
Yes. An equilateral triangle of side s has height h = (s√3)/2, which matches this formula perfectly.

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Reviewed & Authored by: Dr. Elizabeth Vance, PhD Applied Mathematics · Last Updated: 2026-10-06
Computed via classical Euclidean planar polygonal decomposition.