Rectangles, triangles, and trapezoids
What you'll learn
See why a rectangle is width × height, a triangle is half of that, and a trapezoid averages its two bases.
Once you see area as counting unit squares, the formulas for flat shapes stop being something to memorize — each one is just a shortcut for that count.
Rectangle: width × height
A rectangle's squares line up in a neat grid, so you multiply the two sides.
Triangle: half of a rectangle
Draw a diagonal across a rectangle and you split it into two identical triangles. So a triangle is exactly half the rectangle around it: area = (base × height) ÷ 2.
The base (6) and height (3) are the rectangle's sides; the triangle fills half the grid, so 6 × 3 ÷ 2 = 9.
Trapezoid: average the two parallel sides
A trapezoid has two parallel sides of different lengths. Its area is the average of those two sides times the height: ((a + b) ÷ 2) × h — as if you straightened it into a rectangle whose width is the average of the two bases.
Every flat-shape formula is the same idea underneath: count the unit squares, just faster.
Check your understanding
Question 1 of 2
A triangle has a base of 8 and a height of 5. What is its area?