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Triangle area

Find a triangle’s area from its base and perpendicular height.

Practice + answer key · 4 pages

Worksheet settings8 questions · 2 columns · A4
Base and height in cm

The range applies to the base and perpendicular height, not the sloping sides.

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mathsprig-1
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9ede8609
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2 pages
Triangle areaTriangle area. Practice. Find the area of the triangle. Find the area of the triangle. Find the area of the triangle. Find the area of the triangle.Name __________________________Date _______________Triangle areaFind each triangle area.Worked exampleA triangle has base 8 cm and perpendicular height 5 cm. Find its area. → 20cm²Area = base × height ÷ 2.1.Find the area of the triangle.Triangle with base 6 cm and dashed perpendicular height 6 cm, marked with a right angle.6 cm6 cm2.Find the area of the triangle.Triangle with base 7 cm and dashed perpendicular height 3 cm, marked with a right angle.7 cm3 cm3.Find the area of the triangle.Triangle with base 12 cm and dashed perpendicular height 12 cm, marked with a right angle.12 cm12 cm4.Find the area of the triangle.Triangle with base 6 cm and dashed perpendicular height 3 cm, marked with a right angle.6 cm3 cmMathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 2mathsprig-1 · mathsprig-v1 · 9ede8609
Triangle areaTriangle area. Practice. Find the area of the triangle. Find the area of the triangle. Find the area of the triangle. Find the area of the triangle.Name __________________________Date _______________Triangle areaFind each triangle area.5.Find the area of the triangle.Triangle with base 10 cm and dashed perpendicular height 4 cm, marked with a right angle.10 cm4 cm6.Find the area of the triangle.Triangle with base 3 cm and dashed perpendicular height 3 cm, marked with a right angle.3 cm3 cm7.Find the area of the triangle.Triangle with base 3 cm and dashed perpendicular height 5 cm, marked with a right angle.3 cm5 cm8.Find the area of the triangle.Triangle with base 9 cm and dashed perpendicular height 3 cm, marked with a right angle.9 cm3 cmMathSprig · mathsprig.site · support@mathsprig.sitePage 2 of 2mathsprig-1 · mathsprig-v1 · 9ede8609
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Practice + answer key · 4 pages

Geometry

What you’ll practice

Use base × perpendicular height ÷ 2 to find area.

Use the height that meets the base at a right angle, rather than a sloping side. Multiply the base by that height, then divide by two.

How this skill works

Match the dashed perpendicular height to the selected base. The right-angle marker shows that they meet at 90°.

Multiply the base by that height and divide by 2. Use square units.

Worked example

A triangle has base 8 cm and perpendicular height 5 cm. Find its area.
  1. Area = base × height ÷ 2.
  2. 8 × 5 ÷ 2 = 20.
  3. The area is 20 cm².

Answer: 20 cm²

Teaching notes

  • Use the perpendicular height, not the length of a sloping edge.
Practice questions
  1. Find the area of the triangle.

    Triangle with base 6 cm and dashed perpendicular height 6 cm, marked with a right angle.

  2. Find the area of the triangle.

    Triangle with base 7 cm and dashed perpendicular height 3 cm, marked with a right angle.

  3. Find the area of the triangle.

    Triangle with base 12 cm and dashed perpendicular height 12 cm, marked with a right angle.

  4. Find the area of the triangle.

    Triangle with base 6 cm and dashed perpendicular height 3 cm, marked with a right angle.

  5. Find the area of the triangle.

    Triangle with base 10 cm and dashed perpendicular height 4 cm, marked with a right angle.

  6. Find the area of the triangle.

    Triangle with base 3 cm and dashed perpendicular height 3 cm, marked with a right angle.

  7. Find the area of the triangle.

    Triangle with base 3 cm and dashed perpendicular height 5 cm, marked with a right angle.

  8. Find the area of the triangle.

    Triangle with base 9 cm and dashed perpendicular height 3 cm, marked with a right angle.

Answers and steps
  1. 18 cm²
    1. Area = base × perpendicular height ÷ 2 = 6 × 6 ÷ 2 = 18 cm².
  2. 10.5 cm²
    1. Area = base × perpendicular height ÷ 2 = 7 × 3 ÷ 2 = 10.5 cm².
  3. 72 cm²
    1. Area = base × perpendicular height ÷ 2 = 12 × 12 ÷ 2 = 72 cm².
  4. 9 cm²
    1. Area = base × perpendicular height ÷ 2 = 6 × 3 ÷ 2 = 9 cm².
  5. 20 cm²
    1. Area = base × perpendicular height ÷ 2 = 10 × 4 ÷ 2 = 20 cm².
  6. 4.5 cm²
    1. Area = base × perpendicular height ÷ 2 = 3 × 3 ÷ 2 = 4.5 cm².
  7. 7.5 cm²
    1. Area = base × perpendicular height ÷ 2 = 3 × 5 ÷ 2 = 7.5 cm².
  8. 13.5 cm²
    1. Area = base × perpendicular height ÷ 2 = 9 × 3 ÷ 2 = 13.5 cm².