Formulas For Area and Perimeter

Area Formulas

Multiply base by height for parallelograms
Example:
A = bh → A = 8 × 5 → A = 40

Multiply base by height then divide by 2 for triangles
Example:
A = (1/2)bh → A = (1/2)(10 × 6) → A = 30

Add both bases multiply by height then divide by 2 for trapezoids
Example:
A = (1/2)h(b1 + b2) → A = (1/2)(4)(6 + 2) → A = 16

Units

Use regular units when finding perimeter
Use squared units when finding area

Example:
Perimeter = 20 ft
Area = 20 ft²

Area Problems

Identify the shape
Find the base and height
Substitute into the correct formula
Multiply and simplify

Example:
A = bh → A = 7 × 3 → A = 21

Trapezoid

Add the two bases
Multiply the sum by the height
Divide the result by 2

Example:
A = (1/2)(5)(3 + 7) → A = (1/2)(5)(10) → A = 25

Triangle Height Problem

Write the area formula
Substitute known values
Multiply the base by one half
Divide both sides to isolate the height

Example:
A = (1/2)bh
24 = (1/2)(6)h
24 = 3h
h = 8

Coordinate Graph

Plot the points
Connect them to form the shape
Find side lengths by counting units
Add all sides for perimeter
Multiply length and width for area

Example:
Rectangle with length 4 and width 3
Perimeter = 4 + 4 + 3 + 3 = 14
Area = 4 × 3 = 12

Flower Bed Problem

Find the side lengths using coordinates
Multiply each length by the scale factor
Add all sides for perimeter
Multiply length and width for area

Example:
Side lengths 2 and 5, scale factor 3
New lengths 6 and 15
Perimeter = 6 + 6 + 15 + 15 = 42
Area = 6 × 15 = 90

Composite Area

Break the shape into smaller shapes
Find the area of each part
Add all areas together

Example:
Rectangle area = 20
Triangle area = 10
Total area = 30

Shaded Region

Find the area of the outer shape
Find the area of the inner shape
Subtract the inner area from the outer area

Example:
Outer area = 50
Inner area = 20
Shaded area = 30

Summary

Choose the correct formula based on the shape
Always identify base and height correctly
Follow the order of operations
Keep track of units
Break complex shapes into simpler parts
Use subtraction for shaded regions