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Maths · Grade 6 · Set C
A Shape With More Pieces
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C
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Goal: 15 min
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Remember: Cut a shape into rectangles and triangles. Add the areas of the pieces.

Bigger shapes, more thinking

1
The L-shape is cut by an up and down line. What is the area of the left piece in square units?
2
What is the area of the right piece in square units?
3
Cut the same L-shape across instead. The pieces are 27 and 16 square units, and the whole shape is still 43 square units.
TrueFalse
4
This triangle has a base of 8 and a height of 5. What is its area in square units?
5
The house is a rectangle 8 wide and 4 tall with a triangle roof of base 8 and height 3. Which expression gives its area?
8 × 78 × 4 + 8 × 38 × 4 + ½ × 8 × 3
6
What is the area of the house in square units?
7
The shape is cut by the up and down line into a rectangle and a triangle. What is its area in square units?
8
A 6 by 5 rectangle is cut along its diagonal into two triangles. Each triangle has an area of 30 square units.
TrueFalse
9
The steps are cut into three rectangles by the two up and down lines. What is the area of the steps in square units?
10
Join each pair of pieces to the area of the shape they make, in square units.
  1. 1rectangle 7 by 4 and triangle with base 7, height 4
  2. 2rectangle 5 by 5 and triangle with base 5, height 2
  3. 3two triangles, each with base 6 and height 4
  4. 4rectangle 9 by 2 and rectangle 3 by 3
  • A30
  • B24
  • C27
  • D42
11
Circle every way that finds the area of the big L-shape in square units.
28 + 159 × 727 + 1663 − 204 × 7 + 9 × 3
12
Number the steps to find the area of a house made from a rectangle and a triangle roof.
  • Take half of base times height for the roof
  • Multiply wide times tall for the wall
  • Add the wall and the roof
  • Draw a line where the roof meets the wall
13
Pip says a triangle with a base of 6 and a height of 5 has an area of 30 square units. Write how you know Pip is wrong, and what the area is.
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Answer key · Set C
A Shape With More Pieces
128 The left piece is 4 wide and 7 tall: 4 × 7 = 28.
215 The right piece is 5 wide and 3 tall: 5 × 3 = 15.
3True Any way you cut the shape, the pieces add to the same area. 27 + 16 = 43, and 28 + 15 = 43.
420 Half of 8 × 5 = 40 is 20.
58 × 4 + ½ × 8 × 3 The rectangle is 8 × 4. The roof is half of 8 × 3. Add them. 8 × 7 would make the roof a full rectangle.
644 The rectangle is 8 × 4 = 32. The roof is half of 8 × 3 = 24, which is 12. 32 + 12 = 44.
730 The rectangle is 6 × 4 = 24. The triangle has a base of 3 and a height of 4, so its area is half of 12, which is 6. 24 + 6 = 30.
8False The whole rectangle is 6 × 5 = 30. The two triangles share it equally, so each is 15.
936 The pieces are 3 × 6 = 18, 3 × 4 = 12 and 3 × 2 = 6. 18 + 12 + 6 = 36.
101-D, 2-A, 3-B, 4-C Find each piece (a triangle is half of base times height), then add.
1128 + 15, 27 + 16, 63 − 20 28 + 15 and 27 + 16 add the pieces of two different cuts. 63 − 20 takes the missing corner away from the 9 by 7 box. 9 × 7 is the whole box, and 4 × 7 + 9 × 3 counts the corner piece twice.
123, 2, 4, 1 Cut the shape, find each piece, then add.
13Your own words: a grown-up reads it.
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