Area of Triangles & Parallelograms • Topic 1 of 3

Area of Triangle = ½ × base × height

What is Area?

Area is the amount of space inside a 2-dimensional shape. It is measured in square units (cm², m², in², etc.).

Why is Triangle Area Formula ½ × base × height?

A triangle is exactly half of a parallelogram (or rectangle) with the same base and height!

Rectangle area = base × height
Triangle area = ½ × base × height

Important Notes:

Base can be any side of the triangle
Height must be perpendicular (straight up/down) to the base
Height is NOT the slanted side!

TRIANGLE AS HALF A RECTANGLE:

 Rectangle: Triangle:
 ┌─────────────────┐ ╱│
 │ │ ╱ │
 │ │ ╱ │
 │ height │ ╱ │ height
 │ │ ╱ │
 │ │ ╱ │
 └─────────────────┘ ╱______┘
 ←─── base ───→ ← base →
 
 Area = b × h Area = (b × h) ÷ 2


IDENTIFYING BASE AND HEIGHT:

 Acute Triangle: Right Triangle:
 /│ /|
 / │ / |
 / │ / |
 / │h /h |
 / │ / |
 └─────┴─────┘ └─────┘
 base base
 
 Obtuse Triangle (height outside):
 
 /│
 / │ 
 / │ 
 / │ 
 / │ 
 └─────┴─────┘
 base
 (height drawn to extended base)


DIFFERENT BASE CHOICES:

 Same triangle can have different base-height pairs:
 
 Base = b₁ Base = b₂
 height = h₁ height = h₂
 
 /│
 / │ 
 / │ 
 / │h₁
 / │ 
 └──b₁─┴────┘
 
 Area = ½ × b₁ × h₁ = ½ × b₂ × h₂ (always the same!)

Solved Examples

Worked Example

Find the area of a triangle with base 8 cm and height 5 cm.

Solution

A = (1)/(2) × b × h
Area = ½ × 8 × 5
Area = 4 × 5 = 20
Answer: 20 cm²

Worked Example

A triangle has area 30 cm² and base 10 cm. Find its height.

Solution

A = (1)/(2) × b × h
30 = ½ × 10 × h
30 = 5 × h
h = 30 ÷ 5 = 6
Answer: 6 cm

Worked Example

Find the area of a right triangle with legs 6 cm and 8 cm.

Solution

In a right triangle, the legs are perpendicular
Use one leg as base, the other as height
Area = ½ × 6 × 8 = ½ × 48 = 24
Answer: 24 cm²

Key Points

Triangle area = ½ × base × height
Base and height must be perpendicular
Height is NOT the slanted side
Units are square units (²)
Any side can be the base as long as you use its perpendicular height

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The area of a triangle is:

Explanation: $\tfrac12 bh$.

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

Explanation: $\tfrac12\times6\times4$.

Q3.The base and height of a triangle are:

Explanation: Perpendicular.

Q4.Doubling the base ___ the area.

Explanation: Doubles it.

Practice more MCQs → 📝 Assignment · 35 marks