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Grade 6 · Maths · Lessons
Cut it into pieces you know
🏠house shape🟦rectangle🔺triangle➕add areas
Cut it into pieces.
The big ideaCut a shape into rectangles and triangles. Add the areas of the pieces.

How it works

Cut a shape into rectangles and triangles you know. Add the areas of the pieces.

A rectangle's area is base times height. A triangle's area is half of base times height.

Check that the pieces don't overlap and leave no gaps.

Body (rectangle)• 7 × 3 = 21Roof (triangle)• 1/2 × 7 × 4 = 14
A house shape.

Example 1: A house

  1. A house shape has a 7 by 3 body and a triangle roof with base 7 and height 4.
  2. Body: 7 × 3 = 21. Roof: 7 × 4 ÷ 2 = 14.
  3. Add: 21 + 14 = 35 square units.

Example 2: An L shape

  1. Cut an L into an 8 by 3 rectangle and a 4 by 2 rectangle.
  2. 8 × 3 = 24 and 4 × 2 = 8.
  3. Add: 24 + 8 = 32 square units.

Example 3: A trapezoid

  1. Cut a trapezoid into a rectangle 6 by 4 and a triangle with base 2 and height 4.
  2. 6 × 4 = 24 and 2 × 4 ÷ 2 = 4.
  3. Add: 24 + 4 = 28 square units.

Words to know

composite shape
A shape made of simpler shapes.
height
The straight-up distance at a right angle to the base.

Watch out

Try it

  1. A rectangle is 5 by 4 and a triangle has base 5 and height 2. Total area?
  2. What is the area of a triangle with base 6 and height 3?
  3. What do you do with the areas of the pieces?
  4. Why must the pieces not overlap?
Answers: 1. 25 · 2. 9 · 3. add them · 4. so no area is counted twice
For grown-upsDraw an irregular shape on squared paper and find its area by cutting it up.
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