Definition
Area of a triangle
A triangle’s area is half a chosen base times its perpendicular height.
What it means
Copy the triangle and fit the two congruent copies together to make a parallelogram. That parallelogram has area base × perpendicular height. The two triangles share it equally, so one triangle has half that area.
Remember it
Base times straight-up height makes the double; halve it for one triangle.
Example
With base 8 cm and perpendicular height 5 cm, b × h = 40 cm². Half is 20 cm², so A = ½ × 8 × 5 = 20 cm².
Watch for
The height must meet the chosen base line at a right angle; a sloping side is not automatically the height.
Common mix-up
Use the factor ½ once. Halving the base or height and then halving again makes the area too small.
Exact meaning
For any triangle, choose a side as base b and measure perpendicular height h from the opposite vertex to the line containing that base. The area is A = ½bh, expressed in square units.