Perimeter & Area • Topic 1 of 3

1: Area of Rectangles, Squares, Triangles, Parallelograms

What is Perimeter and Area?

  • Perimeter is the total distance around the outside of a figure. Think of it as the length of fence needed to enclose a garden.
  • Area is the amount of surface inside a figure. Think of it as the number of tiles needed to cover a floor.

Area Formulas for Basic Shapes:

ShapeFormulaVariables
Rectangle\(A = l \times w\)\(l\) = length, \(w\) = width
Square\(A = s^2\)\(s\) = side length
Triangle\(A = \frac{1}{2} \times b \times h\)\(b\) = base, \(h\) = height
Parallelogram\(A = b \times h\)\(b\) = base, \(h\) = height (perpendicular)

Perimeter Formulas:

ShapeFormula
Rectangle\(P = 2(l + w)\)
Square\(P = 4s\)
Triangle\(P = a + b + c\) (sum of all sides)
Parallelogram\(P = 2(a + b)\) (where \(a\) and \(b\) are adjacent sides)

Important Notes:

  • In a triangle, height must be perpendicular to the base (forms a right angle)
  • In a parallelogram, the height is the perpendicular distance between the bases
  • Area is always expressed in square units (cm², m², etc.)
  • Perimeter is expressed in linear units (cm, m, etc.)

Real-life Examples:

  • Rectangle: Floor of a room, laptop screen, book cover
  • Square: Chess board, tile, window pane
  • Triangle: Sandwich slice, roof shape, sail of a boat
  • Parallelogram: Leaning bookshelf, diamond shape on a playing card
PERIMETER AND AREA — COMMON SHAPES l b Rectangle P = 2(l+b) A = l x b Square P = 4s, A = s² h Triangle A = (1/2) x b x h r Circle C = 2πr, A = πr² Trapezium: A = (1/2)(a+b)h Parallelogram: A = b x h
Solved Examples
1
Worked Example
Example 1: Find the area and perimeter of a rectangle with length 12 cm and width 7 cm.
Solution- Step 1: Area of rectangle = \(l \times w\) - Step 2: \(A = 12 \times 7 = 84\) cm² - Step 3: Perimeter of rectangle = \(2(l + w)\) - Step 4: \(P = 2(12 + 7) = 2 \times 19 = 38\) cm
2
Worked Example
Example 2: A triangle has a base of 15 cm and height of 8 cm. Find its area. If a parallelogram has the same base and height, find its area.
Solution- Step 1: Area of triangle = \(\frac{1}{2} \times b \times h\) - Step 2: \(A_{triangle} = \frac{1}{2} \times 15 \times 8 = \frac{1}{2} \times 120 = 60\) cm² - Step 3: Area of parallelogram = \(b \times h\) - Step 4: \(A_{parallelogram} = 15 \times 8 = 120\) cm² - Step 5: Notice parallelogram has twice the area of triangle with same base and height
3
Worked Example
Example 3: A square garden has an area of 144 m². Find its side length and perimeter. If a rectangular garden has the same perimeter but length is 5 m more than width, find its dimensions.
Solution- Step 1: Square area \(s^2 = 144\) m² - Step 2: \(s = \sqrt{144} = 12\) m - Step 3: Square perimeter = \(4 \times 12 = 48\) m - Step 4: Rectangle perimeter = \(48 = 2(l + w)\) - Step 5: \(l + w = 24\) - Step 6: Given \(l = w + 5\) - Step 7: Substitute: \((w + 5) + w = 24\) - Step 8: \(2w + 5 = 24\) → \(2w = 19\) → \(w = 9.5\) m - Step 9: \(l = 9.5 + 5 = 14.5\) m

Key Points

  • Rectangle area: \(A = l \times w\) | Perimeter: \(P = 2(l + w)\)
  • Square area: \(A = s^2\) | Perimeter: \(P = 4s\)
  • Triangle area: \(A = \frac{1}{2} \times b \times h\) (height must be perpendicular to base)
  • Parallelogram area: \(A = b \times h\) (height is perpendicular distance between bases)
  • A parallelogram with same base and height as a triangle has twice the area
  • Area uses square units; perimeter uses linear units
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Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.The area of a rectangle is:
Explanation: $l\times b$.
Q2.The area of a square is:
Explanation: side$^2$.
Q3.The area of a triangle is:
Explanation: $\tfrac12 bh$.
Q4.The area of a parallelogram is:
Explanation: base $\times$ height.
Practice more MCQs → 📝 Assignment · 35 marks