Area of triangles
Theory
The area of a triangle is half its base times its perpendicular height: \(A = \dfrac{1}{2} \times b \times h\). Two identical triangles make a parallelogram, so one triangle is half of it.
A triangle has three sides. Its area is the space inside it.
The area is half the base times the perpendicular height: \(A = \dfrac{1}{2} \times b \times h\).
Two identical triangles fit together to make a parallelogram of base \(b\) and height \(h\), so one triangle is half of it.
| Base | Height | Area |
|---|---|---|
| \(10\) cm | \(6\) cm | \(30\) cm\(^2\) |
| \(7\) cm | \(4\) cm | \(14\) cm\(^2\) |
How to find the area of a triangle
- Identify the base and the perpendicular height.
- Multiply base by height, then halve it.
- Write the answer in square units.
| \(A\) | \(=\) | \(\dfrac{1}{2} \times 10 \times 6 = 30\) |
Area \(= 30\) cm\(^2\).
The short sides are base and height.
| \(A\) | \(=\) | \(\dfrac{1}{2} \times 8 \times 5 = 20\) |
Area \(= 20\) cm\(^2\).
| \(A\) | \(=\) | \(\dfrac{1}{2} \times 7 \times 4 = 14\) |
Area \(= 14\) cm\(^2\).
| \(b\) | \(=\) | \(48 \div 6 = 8\) |
Base \(= 8\) cm.
Common pitfalls
Frequently asked questions
What is the area of a triangle?
Half the base times the perpendicular height, \(A = \dfrac{1}{2} \times b \times h\). A base of \(10\) and height of \(6\) give \(30\) square units.
Why is there a half?
Two identical triangles make a parallelogram, so a single triangle is half of it.
What is the height of a triangle?
The perpendicular distance from the base to the opposite corner, measured at a right angle to the base.
How do you find a triangle's area if it is right-angled?
The two shorter sides meet at a right angle, so use them as the base and height in \(\dfrac{1}{2} \times b \times h\).