Geometry & Measurement · Grades 5–8
Area and Perimeter: Formulas for Common Shapes
Rectangles
Area = length × width and perimeter = 2(length + width). Area is in square units, perimeter in plain units.
4 × 5 rectangle
- Perimeter 18
Step-by-step working 4 steps
- 1Area
A = length × width = 4 × 5 = 20
- 2Perimeter
P = 2(l + w) = 2(4 + 5) = 18
- 3Diagonal
d = √(l² + w²) = 6.403124
- 4Units
Area is in square units of whatever length unit you used.
Triangles
A triangle is half of a rectangle with the same base and height: ½ × base × height. A base of 6 and height of 5 gives area 15.
Triangle
Step-by-step working 2 steps
- 1Area
A = ½ × base × height = ½ × 6 × 5 = 15
The height is measured at a right angle to the base.
- 2Units
Area is in square units of whatever length unit you used.
Trapezoids
Average the two parallel sides and multiply by the height. For sides 3 and 5 with height 4: area 16.
Trapezoid
Step-by-step working 2 steps
- 1Area
A = ½(a + b) × h = ½(3 + 5) × 4 = 16
a and b are the two parallel sides.
- 2Units
Area is in square units of whatever length unit you used.
Units
Common mistakes
Using the slanted side as height
Height is perpendicular to the base.
Mixing units
Convert first, then multiply.
Confusing area with perimeter
Area is square units; perimeter is length units.
Frequently asked questions
How do I find the area of an irregular shape?
Split it into rectangles, triangles and trapezoids and add the areas.
