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Parallelogram and trapezoid area

Calculate the area of parallelograms and trapezoids.

Practice + answer key · 4 pages

Worksheet settings8 questions · 2 columns · A4
Dimensions in cm

Select base lengths and perpendicular heights. A range with two values enables trapezoids.

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2 pages
Parallelogram and trapezoid areaParallelogram and trapezoid area. Practice. Find the area of the trapezoid. Find the area of the parallelogram. Find the area of the parallelogram. Find the area of the parallelogram.Name __________________________Date _______________Parallelogram and trapezoid areaFind the area of each labeled shape.Worked exampleA trapezoid has parallel bases 6 cm and 10 cm and perpendicular height 4 cm. →32 cm²Average the bases: (6 + 10) ÷ 2 = 8 cm.1.Find the area of the trapezoid.Trapezoid with parallel bases 8 cm and 10 cm, and perpendicular height 4 cm.10 cm8 cm4 cm2.Find the area of theparallelogram.Parallelogram with base 10 cm and perpendicular height 12 cm.10 cm12 cm3.Find the area of theparallelogram.Parallelogram with base 7 cm and perpendicular height 3 cm.7 cm3 cm4.Find the area of theparallelogram.Parallelogram with base 9 cm and perpendicular height 3 cm.9 cm3 cmMathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 2mathsprig-1 · mathsprig-v1 · 38a4e181
Parallelogram and trapezoid areaParallelogram and trapezoid area. Practice. Find the area of the trapezoid. Find the area of the trapezoid. Find the area of the trapezoid. Find the area of the trapezoid.Name __________________________Date _______________Parallelogram and trapezoid areaFind the area of each labeled shape.5.Find the area of the trapezoid.Trapezoid with parallel bases 12 cm and 5 cm, and perpendicular height 5 cm.5 cm12 cm5 cm6.Find the area of the trapezoid.Trapezoid with parallel bases 6 cm and 7 cm, and perpendicular height 3 cm.7 cm6 cm3 cm7.Find the area of the trapezoid.Trapezoid with parallel bases 3 cm and 4 cm, and perpendicular height 3 cm.4 cm3 cm3 cm8.Find the area of the trapezoid.Trapezoid with parallel bases 9 cm and 11 cm, and perpendicular height 11 cm.11 cm9 cm11 cmMathSprig · mathsprig.site · support@mathsprig.sitePage 2 of 2mathsprig-1 · mathsprig-v1 · 38a4e181
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Practice + answer key · 4 pages

Geometry

What you’ll practice

Choose the correct area rule for a parallelogram or trapezoid.

For a parallelogram, multiply the base by the perpendicular height. For a trapezoid, find the average of the two parallel bases first, then multiply by the height.

How this skill works

Parallelogram area is base × height. A slanted side is not a replacement for the perpendicular height.

Trapezoid area is (base 1 + base 2) × height ÷ 2. The two bases must be the parallel sides.

Worked example

A trapezoid has parallel bases 6 cm and 10 cm and perpendicular height 4 cm.
  1. Average the bases: (6 + 10) ÷ 2 = 8 cm.
  2. Multiply by the height: 8 × 4 = 32 cm².

Answer: 32 cm²

Teaching notes

  • The dashed height and right-angle marker identify the perpendicular measurement.
Practice questions
  1. Find the area of the trapezoid.

    Trapezoid with parallel bases 8 cm and 10 cm, and perpendicular height 4 cm.

  2. Find the area of the parallelogram.

    Parallelogram with base 10 cm and perpendicular height 12 cm.

  3. Find the area of the parallelogram.

    Parallelogram with base 7 cm and perpendicular height 3 cm.

  4. Find the area of the parallelogram.

    Parallelogram with base 9 cm and perpendicular height 3 cm.

  5. Find the area of the trapezoid.

    Trapezoid with parallel bases 12 cm and 5 cm, and perpendicular height 5 cm.

  6. Find the area of the trapezoid.

    Trapezoid with parallel bases 6 cm and 7 cm, and perpendicular height 3 cm.

  7. Find the area of the trapezoid.

    Trapezoid with parallel bases 3 cm and 4 cm, and perpendicular height 3 cm.

  8. Find the area of the trapezoid.

    Trapezoid with parallel bases 9 cm and 11 cm, and perpendicular height 11 cm.

Answers and steps
  1. 36 cm²
    1. Area = (8 + 10) × 4 ÷ 2 = 36 cm².
  2. 120 cm²
    1. Area = base × perpendicular height = 10 × 12 = 120 cm².
  3. 21 cm²
    1. Area = base × perpendicular height = 7 × 3 = 21 cm².
  4. 27 cm²
    1. Area = base × perpendicular height = 9 × 3 = 27 cm².
  5. 42.5 cm²
    1. Area = (12 + 5) × 5 ÷ 2 = 42.5 cm².
  6. 19.5 cm²
    1. Area = (6 + 7) × 3 ÷ 2 = 19.5 cm².
  7. 10.5 cm²
    1. Area = (3 + 4) × 3 ÷ 2 = 10.5 cm².
  8. 110 cm²
    1. Area = (9 + 11) × 11 ÷ 2 = 110 cm².