Question

Use the image to answer the question.

An illustration shows a polygon where the top, right, and bottom sides are perpendicular to each other. A smaller rectangular piece is missing from the center of the left side of the polygon inward. The dimensions are as follows: the top side is 6, the right side is 8, and the bottom side is 6. The left side is divided into three parts. It shows a vertical width of 2 from the top

Solve the following problem using what you know about composite figures. What is the area of the figure?

(1 point)
Responses

36 square units
36 square units

24 square units
24 square units

48 square units
48 square units

30 square units
30 square units
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Question
Use the image to answer the question.

A composite figure is comprised of a rectangle and two congruent right triangle on either side. The triangle have a height of 4 inches and a width of 3 inches.

The composite shape in the image has an area of 40 square inches. What is the area of the rectangle within the composite shape?

(1 point)
Responses

16 square inches
16 square inches

28 square inches
28 square inches

34 square inches
34 square inches

7 square inches
7 square inches
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Question
Use the image to answer the question.

A composite shape is drawn with a rectangle and a square. All lines are straight and all corners are marked as right angles. The shape is made with a vertically aligned rectangle 8 yards in length and 7 yards in width. A horizontally aligned rectangle 3 yards wide and of unknown length is removed from the bottom left corner of the original rectangle. The remaining width along the bottom right is 3 yards.

Solve the following problem: A town has a swimming pool shaped as in the diagram.
What is the area of the swimming pool in square yards?

(1 point)
Responses

44 square yards
44 square yards

65 square yards
65 square yards

30 square yards
30 square yards

56 square yards
56 square yards
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Answer 1

Here are the answers with quick work:

1) Area = 36 square units.
- Treat the shape as a 6×8 rectangle (area 48) with a 3×4 rectangular notch removed.
- Notch area = 3·4 = 12, so remaining area = 48 − 12 = 36.

2) Rectangle area = 28 square inches.
- Each right triangle area = 1/2·3·4 = 6, two triangles = 12.
- Rectangle area = total 40 − 12 = 28.

3) Pool area = 44 square yards.
- Original rectangle = 7·8 = 56.
- Removed corner rectangle = 4·3 = 12 (since bottom remainder is 3, removed width = 7−3 = 4).
- Remaining area = 56 − 12 = 44.