Example 1
\(b = 8, h = 6 \rightarrow A = 0.5 \times 8 \times 6 = 24\text{ units}^2\)
Triangle Area Calculator
Calculate the area of a triangle using base and height with detailed step-by-step solution.
Explore how the triangle's area changes
Drag the base and height sliders to reshape the triangle. The area updates instantly so you can see how each dimension contributes.
Quick presets
10.00
1.0020.00
5.00
1.0020.00
Predict what will happen
What if you halve the base and double the height?
Try base = 5, height = 20 versus base = 10, height = 10.
Try this
Find a base/height pair where the area is exactly 30. There are infinitely many — drag the sliders to find at least three.
Why it works
Imagine the triangle inside a rectangle that has the same base and the same height. Two copies of the triangle exactly fill the rectangle, so the triangle is half the rectangle's area: ½ · b · h.
Notice
Only the perpendicular height counts. A skewed triangle with the same base and the same vertical reach has the same area, even if the slanted side gets longer.
Results
Final Answer
Area is \(A = 25.00\)
Step-by-step Solution
- The formula for the area of a triangle is \(A = \frac{1}{2} \times b \times h\)
- Substitute the given values: \(A = 0.5 \times 10.00 \times 5.00\)
- Perform the multiplication: \(A = 25.00\)
base
\(b = 10.00\)
height
\(h = 5.00\)
A
\(A = 25.00\)
Theory & Formula
The area of a triangle is the space enclosed by its three sides. It's calculated using the base and height.
The area A of a triangle with base b and height h is given by:
\(A = \frac{1}{2} \times b \times h\)
This formula works because a triangle is essentially half of a parallelogram with the same base and height.
Alternative formulas
- From sides and included angle:
A = (1/2)ab sin C - From three sides (Heron's formula):
A = √(s(s-a)(s-b)(s-c)), wheres = (a+b+c)/2
\(A = \frac{1}{2} \times b \times h\)
Worked Examples
Example 2
\(b = 15, h = 4 \rightarrow A = 0.5 \times 15 \times 4 = 30\text{ units}^2\)
Heron's Formula
\(A = \sqrt{s(s-a)(s-b)(s-c)}\) \text{ where } \(s = \frac{a+b+c}{2}\)
External educational resource
Construct triangles in GeoGebra
Open the GeoGebra geometry tool to draw triangles, measure base and height, and confirm the area formula by dragging vertices.
GeoGebra (geogebra.org)