Area of a Triangle
\text{Area of rectangle} = l \times wTranscript
Today we find the area of any triangle using a simple formula. Let's start with a rectangle. Its area is length times width.
\text{Area of rectangle} = l \times wNow watch what happens when we draw a diagonal across the rectangle. The diagonal cuts the rectangle into two equal triangles. So each triangle has half the area of the rectangle.
- Diagonal splits rectangle in half
\text{Area of triangle} = \frac{1}{2} \times l \times wWe call the length the base and the width the height. So the formula becomes: area equals one half times base times height.
- base = b, height = h
A = \frac{1}{2} \times b \times hLet me show you with real numbers. Say base is six and height is four. Area equals one half times six times four.
A = \frac{1}{2} \times 6 \times 4 = \frac{24}{2} = 12The height must be perpendicular to the base, like a vertical line. This formula works for any triangle, not just right triangles. Quick check: if base is eight and height is five, what is the area?
- Height is perpendicular to base
Remember: area of a triangle is always half the base times the height.
Quick quiz
Q1. Base = 8, height = 5. What is the area?
Half times 8 times 5 equals 20 square units.
