Area of Triangles & Parallelograms • Topic 2 of 3

Area of Parallelogram = base × height

What is a Parallelogram?

A parallelogram is a quadrilateral with two pairs of parallel sides.

Why is Parallelogram A = b × h?

A parallelogram can be transformed into a rectangle with the same base and height!

Cut here →  ┌────────────┐
           │            │
           │            │  Move triangle
           │            │  to other side
           └────────────┘
           
           ┌────────────┐
           │░░░░░░░░░░░░│  →  ┌────────────┐
           │░░░░░░░░░░░░│     │░░░░░░░░░░░░│
           └────────────┘     └────────────┘
           ┌────────────┐
           │            │
           │            │
           └────────────┘
           
           Result: Rectangle with same base and height!

Important Notes:

Height must be perpendicular to the base
Height is NOT the slanted side length
Base can be any side of the parallelogram

PARALLELOGRAM AREA VISUAL:

    Parallelogram:              Rectangle (same area):
    
         /─────────────────/         ┌─────────────────┐
        /                 /          │                 │
       /                 /           │                 │
      /                 /            │                 │
     /                 /             │                 │
    /─────────────────/              └─────────────────┘
    ←──── base ────→                 ←──── base ────→
         ↑ height                        ↑ height
         (perpendicular)


FINDING BASE AND HEIGHT:

    Correct:                    Wrong:
    
         /│─────/                  /───────/
        / │     /                 /       /
       /  │h   /                 /       /
      /   │   /                  /       /
     /    │  /                   /       /
    /_____│_/                    /_______/
    ←─b─→                       ←─b─→
    
    Height is perpendicular    Height is slanted (wrong!)
    to the base!


AREA CALCULATION STEPS:

    Given: base = 7 cm, slanted side = 5 cm, height = 4 cm
    
    Area = base × height = 7 × 4 = 28 cm²
    
    (The slanted side length 5 cm is NOT used!)

Solved Examples

Worked Example

Find the area of a parallelogram with base 9 m and height 5 m.

Solution

A = b × h
Area = 9 × 5 = 45
Answer: 45 m²

Worked Example

A parallelogram has area 84 cm² and height 7 cm. Find its base.

Solution

A = b × h
84 = base × 7
base = 84 ÷ 7 = 12
Answer: 12 cm

Worked Example

Find the area of a rhombus (a type of parallelogram) with base 6 in and height 4 in.

Solution

A = b × h = 6 × 4 = 24
Answer: 24 in²

Worked Example

A parallelogram has base 10 cm and slanted side 8 cm. The perpendicular height is 6 cm. Find area.

Solution

Use base and perpendicular height (ignore slanted side!)
Area = 10 × 6 = 60
Answer: 60 cm²

Key Points

Parallelogram area = base × height
Height must be perpendicular to base
Ignore slanted side lengths
Transform into rectangle to understand formula
Units are square units (²)

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The area of a parallelogram is:

Explanation: base $\times$ height.

Q2.For base $6$ and height $4$, the area is:

Explanation: $6\times4$.

Q3.The height is ___ to the base.

Explanation: Perpendicular.

Q4.A triangle on the same base and height as a parallelogram has ___ its area.

Explanation: Half.

Practice more MCQs → 📝 Assignment · 35 marks