Area of Rectangles & Triangles
“Area counts the squares inside — rectangle is width×height, triangle is half of that.”
The formula
▭ S = a × b △ S = c × h ÷ 2How to read it: A rectangle's area is width times height; a triangle's area is base times height divided by 2
- a
- — the rectangle's width
- b
- — the rectangle's height
- c
- — the triangle's base
- h
- — the triangle's height — the straight-up distance from base to top
The hook
How many tiles cover the floor? Area measures how much flat space a shape takes up.
In plain words
The amount of flat space a shape covers, counted as how many unit squares fit inside.
The intuition
Fill a rectangle with 1 cm squares: each row holds 'width' squares, and there are 'height' such rows. So area = width × height. A triangle is exactly half of a matching rectangle, so it's base × height ÷ 2.
How it's built
Rectangle: multiply width by height. Triangle: multiply the base by the height (straight up from that base), then divide by 2. The height is the straight-up distance, not the slanted side.
Example
Rectangle 5 by 3: 5 × 3 = 15. Triangle with base 6 and height 4: 6 × 4 ÷ 2 = 12.
Common mistake
Don't forget to divide by 2 for a triangle. 6 × 4 = 24 is the rectangle; the triangle is half of that, 12.
Where it's used
Measuring floors and walls, working out paint, tiles, or grass needed, sizing land.
Where it came from
The ancient Egyptians grew skilled at area to re-measure fields for taxes after the Nile flooded.
Prerequisites
Quick check
What is the area of a rectangle 6 wide and 4 tall?
- 10
- 20
- 24✓
- 48
Practice
Find the area of a rectangle 7 by 2.
Answer: 14
- Area = width × height
- 7 × 2 = 14
Takeaway: Rectangle area = width × height.
Find the area of a triangle with base 10 and height 4.
Answer: 20
- Area = base × height ÷ 2
- 10 × 4 = 40
- 40 ÷ 2 = 20
Takeaway: A triangle is half its rectangle.
Find the area of a square with side 5.
Answer: 25
- A square has equal sides.
- 5 × 5 = 25
Takeaway: Square area = side × side.