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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Now an L-shape made of a 5 ft by 4 ft rectangle and a 3 ft by 2 ft rectangle. First rectangle: 5 × 4 = 20 square feet. Second rectangle: 3 × 2 = 6 square feet. Are they joined or cut out? Joined, so we add: 20 + 6 = 26 square feet. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartIn the formula A = ½(b₁ + b₂) × h, what do b₁ and b₂ stand for?

   1. AThe two parallel sides
   2. BThe two slanted sides
   3. CThe base and the height
   4. DThe perimeter and the height

   How do you know?
3. 3

   Warm restartWhat is the area of a trapezoid with bases 6 cm and 10 cm and height 4 cm?

   1. A32 square cm
   2. B64 square cm
   3. C20 square cm
   4. D240 square cm

   How do you know?
4. 4

   Warm restartWhat is the area of a trapezoid with bases 5 cm and 9 cm and height 6 cm?

   1. A42 square cm
   2. B84 square cm
   3. C20 square cm
   4. D270 square cm

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughWhat is the area of the top of the T?

   1. A56 sq ft
   2. B36 sq ft
   3. C60 sq ft
   4. D18 sq ft

   Why is that the answer?
2. 6

   Think it throughWhat is the total area of the T-shaped room?

   1. A116 sq ft
   2. B104 sq ft
   3. C96 sq ft
   4. D840 sq ft

   How do you know? Give a second reason as well.
3. 7

   Think it throughWhat will the carpet cost?

   1. A$580
   2. B$116
   3. C$300
   4. D$1,160

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelFor the U-shaped pool, why did we subtract instead of add? When do you add areas and when do you subtract?

Use the words

Fill each blank with a word from the bank.

• The space inside a figure made of basic shapes, found with A = A₁ + A₂, is the ___.
• A shape made of two or more basic shapes combined is a ___.
• To break a composite figure into basic shapes is to ___ it.
• To find the total area of separate parts, I ___ their areas.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: A common mistake in Area of Composite Figures is adding every piece even when a piece has been cut out of the figure.
2. 10

   Say moreFor the U-shaped pool you subtracted a 6 ft by 4 ft cutout from a 14 ft by 10 ft rectangle. How do you decide when to ADD areas and when to SUBTRACT?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: This is an L-shaped room from a floor plan. A dashed line splits it into two rectangles, and each part is labeled with its length and width.

   Show your work

Last check

These two come from Lesson 5.3. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A composite figure is made of a 9 ft x 7 ft rectangle and a 3 ft x 4 ft rectangle joined together. What is the total area?

   1. A75 sq ft
   2. B63 sq ft
   3. C12 sq ft
   4. D75 ft

   Explain your choice.
2. 13

   From Lesson 5.3Explain your thinking — A trapezoid has bases of 9 inches and 5 inches, and a height of 6 inches. What is its area?

   1. A42 sq in
   2. B84 sq in
   3. C27 sq in
   4. D42 in

   How do you know?
3. 14

   From Lesson 5.3Why add the two parallel edges and then take half?

   1. ABecause the average of the two bases acts like one rectangle's width
   2. BBecause trapezoids are half of rectangles
   3. CBecause 20 + 12 = 32 is easier
   4. DBecause the height must be halved

   How do you know?

Be honest — this tells your teacher what to do next