A triangle is half of a parallelogram, and that tells you its area.
Key idea
The area of a triangle is half of base times height: $A = \frac{1}{2}bh$. The height is measured at a right angle to the base, from the opposite corner.
Why it works
Take two copies of any triangle and turn one of them halfway around. They fit together into a parallelogram with the same base and the same height. The parallelogram's area is $bh$, and the triangle is exactly half of it, so its area is $\frac{1}{2}bh$.
Worked example: Base and height
A triangle has base 10 m and height 6 m. Find its area.
- $A = \frac{1}{2} \times 10 \times 6$.
- $\frac{1}{2} \times 60 = 30$.
Answer: 30 square meters
Worked example: A right triangle
A right triangle has sides 6, 8 and 10 inches. Find its area.
- The two sides that meet at the right angle, 6 and 8, are a base and its height.
- $A = \frac{1}{2} \times 6 \times 8 = 24$. The 10-inch side is slanted and not needed.
Answer: 24 square inches
Worked example: The height outside the triangle
A triangle has a base of 5 cm. The height from the top corner, 4 cm, falls outside the triangle, on the extended base. Find the area.
- The height still meets the line of the base at a right angle; it just lands beyond the base.
- $A = \frac{1}{2} \times 5 \times 4 = 10$.
Answer: 10 square centimeters
Common mistake
Forgetting the $\frac{1}{2}$, or using a slanted side as the height. Quick check: the triangle fits inside a rectangle that is $b$ wide and $h$ tall, so its area must be less than $b \times h$. If your answer equals $b \times h$, you forgot the half.