Area of compound shapes · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Finding the area of compound shapes

Mathematics · Measurement · ages 8-9
Name ______________________   Date ____________

  1. Work out 3 x 5 + 2 x 4.

    Answer: ______________

  2. An L-shape splits into a 3 m by 5 m rectangle and a 2 m by 4 m rectangle. What is the total area?

    • 23 square metres
    • 15 square metres
    • 21 square metres
    • 19 square metres

  3. To find the area of an L-shaped figure, what should you do first?

    • Split it into rectangles
    • Measure only the longest side
    • Multiply all the side lengths together

  4. A floor plan is shaped like a T. How many rectangles do you usually split it into?

    • 1
    • 2
    • 4

  5. A T shape splits into 4 by 3 and 2 by 5 rectangles. What is its total area?

    Answer: ______________

  6. A T-shaped floor plan is split into a 2m by 6m rectangle and a 3m by 2m rectangle. What is the total area?

    • 12 sq m
    • 18 sq m
    • 6 sq m

  7. Which plan finds an L-shape area?

    • Guess from the longest side
    • Split into rectangles, find each, add
    • Measure one rectangle only
    • Add all the side lengths

  8. Ben splits an L-shape with overlapping parts and adds both. He says overlaps do not matter. Is Ben right?

    Circle one:   True   False

  9. Mia splits an L-shape into a 5m by 2m rectangle and a 3m by 4m rectangle. She finds 10 sq m and 12 sq m, then writes the total area as 10 sq m. What went wrong?

    • She multiplied wrong
    • She used the wrong shape
    • She forgot to add the two areas together

  10. A playground is T-shaped: a 10 m by 6 m band plus a 4 m by 5 m stem. What is the total area in square metres?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Finding the area of compound shapes W1-mt_eMtV6tBSJm-s1

  1. 23 · 3 x 5 + 2 x 4 = 23 because 15 + 8 = 23.
  2. 23 square metres · 23 square metres is correct because 3 x 5 = 15 and 2 x 4 = 8, and 15 + 8 = 23.
  3. Split it into rectangles · An L-shape is made of rectangles joined together. Split it into rectangles you can measure, then add their areas.
  4. 2 · A T-shape can be split into two rectangles: one for the top bar and one for the stem.
  5. 22 · The total is 22 because 4 x 3 = 12 and 2 x 5 = 10, and 12 + 10 = 22.
  6. 18 sq m · 2 x 6 = 12 and 3 x 2 = 6. Add both parts: 12 + 6 = 18 square meters.
  7. Split into rectangles, find each, add · Split into rectangles, find each, add is the plan. Guessing, measuring one block, or adding lengths all miss cover.
  8. False · Ben is wrong because overlapped squares get counted twice, inflating the total.
  9. She forgot to add the two areas together · She found both areas correctly but stopped before adding them. The total should be 10 + 12 = 22 square meters.
  10. 80 · The total is 80 square metres because 10 x 6 = 60 and 4 x 5 = 20, and 60 + 20 = 80.
Worksheet · LightMySky