2D Shapes
Master perimeter and area of simple and composite shapes
This document provides an overview of the essential formulas and concepts related to 2D shapes. Learn to calculate perimeter and area of squares, rectangles, triangles, circles, and more.
Learning Outcomes
- Calculate perimeter and area of squares, rectangles, triangles, and circles
- Find perimeter and area of parallelograms, trapeziums, and rhombuses/kites
- Identify and use perpendicular height correctly
- Break down composite shapes into simpler components
- Work backwards to find missing dimensions given area or perimeter
- Apply unit consistency in all calculations
Shape Gallery
Core 2D Shape Formulas
| Shape | Perimeter Formula | Area Formula |
|---|---|---|
| Square | P = 4a | A = a² |
| Rectangle | P = 2(l + w) | A = l × w |
| Triangle | P = a + b + c | A = ½ × b × h |
| Circle | C = 2πr | A = πr² |
| Parallelogram | P = 2(a + b) | A = b × h |
| Trapezium | P = a + b + c + d | A = ½ × (a + b) × h |
| Rhombus/Kite | P = 4a | A = ½ × d₁ × d₂ |
Quiz 1 - Shape Formulas
What is the area formula for a triangle
Key Concepts
Perpendicular Height
For triangles and parallelograms, always use the height that is perpendicular (90° angle) to the base. This is crucial for accurate area calculations.
Composite Shapes
Complex figures can often be broken down into simpler shapes like rectangles, triangles, or semi-circles for easier calculation.
Working Backwards
Sometimes you need to find a missing dimension (like radius or length) when the area or perimeter is provided. Rearrange formulas to solve for the unknown.
Unit Consistency
Ensure all dimensions are in the same unit (e.g., all in cm or all in m) before starting calculations.
Example Problems
Example 1: Area of a Rectangle
Length = 5 cm, Width = 3 cm. Find Area.
Example 2: Perimeter of a Triangle
Sides = 3 cm, 4 cm, 5 cm. Find Perimeter.
Example 3: Area of a Composite Shape
Rectangle (6 cm × 4 cm) with semi-circle (diameter 4 cm). Find total area.
- Rectangle area: 6 × 4 = 24 cm²
- Semi-circle radius: r = 4/2 = 2 cm
- Semi-circle area: ½ × π × 2² = 2π cm² ≈ 6.28 cm²
- Total area: 24 + 6.28 = 30.28 cm²
Quiz 2 - Composite Shapes
A rectangle 8 cm × 3 cm has a triangle on top (base 8 cm, height 4 cm). Total area
Practical Applications
Architecture & Construction
Calculating area of land or perimeter of buildings for planning and resource allocation.
Gardening & Landscaping
Determining area of garden beds or perimeter of fences for material estimation.
Art & Design
Calculating canvas area or frame perimeter for proper fitting.
Practice & Assess
Test your knowledge with these interactive games.
Match - Shape to Formula
Fill - Circle Area
Area of circle = π × ___²
Practice Questions
Square with side 6 cm. Find area and perimeter.
Rectangle length 8 cm, width 5 cm. Find area.
Triangle base 10 cm, height 6 cm. Find area.
Circle radius 7 cm. Find area (π ≈ 22/7).
Parallelogram base 12 cm, height 5 cm. Find area.
Trapezium parallel sides 6 cm and 10 cm, height 4 cm. Find area.
