Triangle Area Calculator
Calculate the area of a triangle using base and height.
How to find the area of a triangle
The most common way to find a triangle's area is half its base times its height. The key detail people miss is that the height must be the perpendicular distance from the base to the opposite corner, not the length of a slanted side. This works for every triangle, whatever its shape.
$$A = \frac{1}{2} \times b \times h$$
How to use this calculator
- Enter the base length.
- Enter the perpendicular height.
- Press Calculate to get the area.
Worked example
A triangle with a base of 10 and a height of 4 has an area of one half times 10 times 4, which is 20 square units. Notice it does not matter whether the triangle leans to one side; only the base and perpendicular height count.
How to use this calculator
- Measure or enter the base of the triangle.
- Measure or enter the perpendicular height for that same base.
- Multiply the base by the height, then divide by 2.
- Read the result as the triangle's area in square units.
The formula explained
$$ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $$
- \(\text{Area}\) = the area of the triangle
- \(\text{base}\) = the length of the triangle's base
- \(\text{height}\) = the perpendicular height from the base to the opposite corner
Step by step method
- Identify one side as the base.
- Find the perpendicular height to that base, not a slanted side.
- Multiply base by height to get the area of the surrounding rectangle or parallelogram idea.
- Divide by 2 because a triangle is half of that shape.
Worked example
Suppose a triangle has a base of 12 cm and a height of 7 cm.
- Use the formula \(\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\).
- Substitute the values: \(\text{Area} = \frac{1}{2} \times 12 \times 7\).
- Compute the result: \(12 \times 7 = 84\), then half of 84 is 42.
Answer. The area is 42 square cm.
Tips and common mistakes
- Make sure the height is perpendicular to the base, not just any side length.
- Use the same unit for both measurements, such as cm or m.
- The answer is always in square units, not linear units.
- If you know a slanted side instead of the height, you cannot use this calculator directly.
Frequently asked questions
What is the perpendicular height?+
It is the straight-line distance from the base to the opposite vertex, measured at a right angle to the base. For a slanted triangle this is not the same as the length of the sloping side, which is a common mistake.
What if I only know the three side lengths?+
Then you can use Heron's formula instead, which finds the area from the three sides alone. It is handy when no height is given, and we have a separate calculator for it.
Why is there a one half in the formula?+
A triangle is exactly half of a rectangle with the same base and height. Picture the rectangle, then cut it along the diagonal and you get two equal triangles, which is where the one half comes from.
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