Maths · Geometry & Measures
Area of triangles & parallelograms
Apply area formulae to non-rectangular shapes.
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Area of a Triangle
The area of any triangle is half the base times the perpendicular height. The formula is: Area = ½ × base × height. The height must meet the base at a right angle.
Area of a Parallelogram
A parallelogram is a four-sided shape with opposite sides parallel and equal. Its area equals base times perpendicular height: Area = base × height. The height is always measured at right angles to the base.
Choosing the Base and Height
Any side can be the base. Once you pick a base, the height is the perpendicular distance to the opposite side or vertex. Make sure height and base are perpendicular.
Units Squared
Area is measured in square units like cm² or m². When you multiply two lengths, the units multiply too. So 5 cm × 3 cm = 15 cm².
Worked examples
1. Find the area of a triangle with base 8 cm and height 5 cm.
- Use the formula: Area = ½ × base × height.
- Area = ½ × 8 × 5.
- Area = ½ × 40 = 20 cm².
2. A parallelogram has a base of 12 m and perpendicular height of 7 m. Find its area.
- Use the formula: Area = base × height.
- Area = 12 × 7.
- Area = 84 m².
3. A triangle has base 6.5 cm and height 4 cm. Calculate the area.
- Area = ½ × base × height.
- Area = ½ × 6.5 × 4 = ½ × 26.
- Area = 13 cm².
Try it yourself
A parallelogram has a base of 9 cm and height of 6 cm. What is its area?
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