Example 1
- Base: 10
- Height: 6
30.00
a = 10 and h = 6 gives 30.00.
Triangle area calculator
Type the base and the height perpendicular to it. The calculator takes half the product and shows area in cm² or in², matching the unit switch.
A = ½bh. Equilateral is on the equilateral triangle area calculator. Pythagoras is on the Pythagorean theorem page.
Result
Base a (cm) and Height h (cm). Area shows up here.
How it works
Triangle area is half the base times the height that drops perpendicular to that base. The neighboring 10 by 5 rectangle has area 50.
The same 10 and 5 here give 25.00, exactly half. The first card example starts at 10 and 6, which is 30.00, because 10 times 6 divided by two.
A square and a rectangle do not divide by two. A triangle with base 8 and height 5 has 20.00. At 20 and 5 you get 50.00, half of the 20 by 5 rectangle, which itself is 100. An equilateral triangle with one side lives on another page: there (√3/4)a², here two fields a and h.
The calculator does not run when the base or the height is missing. A typed zero can yield zero, but that is not a figure from a workbook.
Switching to inches relabels the result as in² and does not convert a typed 10 into inches. Heron from three sides is not printed here: you need h first.
Measure height perpendicular to the base you chose. A slanted edge is not h. Pythagoras gives a missing side, not area. At 9 and 9 you get 40.50: that is still ½ah, not equilateral, because an equilateral of side 9 has a different height.
How to use
- Type base a, for example a lot edge or a side from a homework row, in cm or inches.
- Type height h in the same unit, perpendicular to that base, not a slanted arm.
- Click Calculate. The result uses two decimal places and cm² or in².
- If you only know an equilateral side, open that page. This page stays with two dimensions, a and h.
- The 10 and 6 example is 30.00. Classic 10 and 5 is 25.00, half of the 10 by 5 rectangle, not the sum 15.
Formula
A = ½ × a × h
Not the equilateral formula (√3/4)a².
A = ½ah at 10 and 6
Half the product of base and height. a = 10 and h = 6 give 30.00. a = 8 and h = 5 give 20.00. Not (√3/4)a².
- A
- Area ½ah. 10 × 6 / 2 = 30.00. 12 × 7 / 2 = 42.00. 6 × 4 / 2 = 12.00.
- a
- Base. 10 with h = 6 is 30. The equilateral page takes a side alone.
- h
- Height perpendicular to a. 6 with a = 10. 5 with a = 8 is 20.00.
Examples
Example 2
- Base: 8
- Height: 5
20.00
a = 8 and h = 5 gives 20.00.
Example 3
- Base: 12
- Height: 7
42.00
a = 12 and h = 7 gives 42.00.
Example 4
- Base: 6
- Height: 4
12.00
a = 6 and h = 4 gives 12.00.
Example 5
- Base: 15
- Height: 8
60.00
a = 15 and h = 8 gives 60.00.
Example 6
- Base: 9
- Height: 9
40.50
a = 9 and h = 9 gives 40.50.
Example 7
- Base: 20
- Height: 5
50.00
a = 20 and h = 5 gives 50.00.
Example 8
- Base: 4
- Height: 3
6.00
a = 4 and h = 3 gives 6.00.
Frequently asked questions
Does a 10 by 5 triangle have area 25?
Yes. 10 times 5 divided by two is 25.00, half of the 10 by 5 rectangle, which is 50. The first card example is 10 and 6, then 30.00.
Why do 10 and 6 give 30, not 60?
Because of the half. 10 times 6 is a rectangle of 60. The triangle with that base and height is 30.00.
Is this the equilateral triangle card?
No. That page takes one side and (√3/4)a². Here you type base and height. Side 10 on the equilateral page is a different area than 10 and 6 here.
Is Heron from three sides on this page?
No. Only ½ah. Three sides without height belong elsewhere, or you find h first.
What if I leave height empty?
Nothing is computed. Type h or load the 10 and 6 example. A typed zero is not guessed for you as “no triangle”.
Can height be slanted?
The formula assumes h is perpendicular to a. A slanted edge is not h. A wrong h spoils 25.00 or 30.00, not the code.
Does Pythagoras replace ½ah?
No. Pythagoras gives a side. Area still needs a base and a height, or another area formula.
Can I mix centimeters and inches?
Not in one run. Both dimensions in cm or both in inches. The unit switch changes the result label and does not convert typed numbers.
Why do 9 and 9 give 40.50 if it looks equilateral?
Height 9 on base 9 does not have to be equilateral. The formula is still ½ah. An equilateral of side 9 has a different h.
Is a 20 by 5 rectangle the same 50?
A 20 by 5 rectangle is 100. A triangle 20 and 5 is 50, half. Two cards, two formulas.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.