Area of a Triangle
Learning the formula and how to calculate the area of triangles
1. Triangle and Its Related Rectangle
Every triangle is exactly half of its related rectangle: the rectangle with the same base and the same height as the triangle.
Visual Demonstration
The area of triangle ACD is half the area of rectangle ABCD
The blue area is equal to the yellow area
Area of Triangle ACD = ½ × Area of Rectangle ABCD
= ½ × 6 cm × 4 cm = ½ × 24 cm² = 12 cm²
2. The Area Formula
Area of Triangle Formula
or written as: Area = (base × height) ÷ 2
Remember:
- The base and height must be perpendicular (at 90°)
- Always use the perpendicular height, not the slanted side
- Area is measured in square units (cm², m², etc.)
3. Worked Examples
Example 1: Acute-angled Triangle
Find the area of Triangle M with base 10 cm and height 8 cm.
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Solution:
Area of Triangle M
= ½ × base × height
= ½ × 10 cm × 8 cm
= ½ × 80 cm²
= 40 cm²
Example 2: Right-angled Triangle
Find the area of Triangle J with base 6 cm and height 6 cm.
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Solution:
Area of Triangle J
= ½ × base × height
= ½ × 6 cm × 6 cm
= ½ × 36 cm²
= 18 cm²
4. Practice Questions
Practice 1:
Find the area of a triangle with base 12 cm and height 8 cm.
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Area = ½ × 12 × 8 = ½ × 96 = 48 cm²
Practice 2:
A triangle has an area of 30 cm² and a base of 10 cm. What is the height?
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Area = ½ × base × height, so base × height is twice the area.
Base × height = 2 × 30 = 60
The base is 10 cm, so the height is 60 ÷ 10.
Height = 60 ÷ 10 = 6 cm
Practice 3:
Find the area of this triangle with base 17 m and height 14 m.
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Area = ½ × 17 × 14 = ½ × 238 = 119 m²
Note: Even though the height is outside the triangle, we still use the same formula!
Key Takeaways
- A triangle is half of its related rectangle
- Area of Triangle = ½ × base × height
- The base and height must be perpendicular (at 90°)
- The formula works for ALL triangles: acute-angled, right-angled and obtuse-angled
- Area is always in square units (cm², m², km²)