Question

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)Responses48 square units24 square units30 square units36 square units

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the area of the figure, we first need to find the missing dimensions. Since the top side is 6, the right side is 8, and the bottom side is 6, the missing dimensions on the left side can be calculated as follows:

Total left side = 6
Vertical width = 2
Missing width = Total left side - Vertical width = 6 - 2 = 4

Now, to find the area of the figure, we need to calculate the area of the larger rectangle (6 x 8 = 48) and subtract the area of the missing rectangle (4 x 2 = 8).

Area of figure = 48 - 8 = 40 square units

Therefore, the correct answer is:
30 square units

Answer 2

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

34 square inches
34 square inches

16 square inches
16 square inches

7 square inches
7 square inches

28 square inches
28 square inches
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Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the area of the rectangle within the composite shape, we first need to find the total area of the composite shape and then subtract the area of the two right triangles.

Each triangle has a height of 4 inches and a base of 3 inches, so the area of one triangle is 1/2 * base * height = 1/2 * 3 * 4 = 6 square inches. Since there are two congruent triangles, the total area of both triangles is 6 + 6 = 12 square inches.

The total area of the composite shape is given as 40 square inches.

Now, to find the area of the rectangle, we subtract the area of the triangles from the total area of the composite shape:

Area of rectangle = Total area of composite shape - Area of triangles
Area of rectangle = 40 square inches - 12 square inches
Area of rectangle = 28 square inches

Therefore, the area of the rectangle within the composite shape is 28 square inches.

The correct answer is:
28 square inches

Answer 4

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

65 square yards
65 square yards

44 square yards
44 square yards

30 square yards
30 square yards

56 square yards
56 square yards
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Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the area of the swimming pool, we first need to calculate the total area of the original vertically aligned rectangle and then subtract the area of the horizontally aligned rectangle that was removed.

The area of the original vertically aligned rectangle is calculated as length * width = 8 * 7 = 56 square yards.

Given that a horizontally aligned rectangle with a width of 3 yards is removed from the bottom left corner, the length of this removed rectangle can be calculated as 7 - 3 = 4 yards.

The area of the removed rectangle is 4 * 3 = 12 square yards.

Finally, to find the area of the swimming pool, we subtract the area of the removed rectangle from the total area of the original rectangle:
Area of swimming pool = Total area of original rectangle - Area of removed rectangle
Area of swimming pool = 56 square yards - 12 square yards = 44 square yards

Therefore, the correct answer is:
44 square yards

Answer 6

Use the image to answer the question.

A composite shape is drawn using a rectangle and a triangle. The rectangle has a base labeled as 6 centimeters. A triangle showing a perpendicular height of 6 centimeters is stacked on the top side of the rectangle. The base of the triangle and the top of the rectangle have a common side. Right angle symbols are shown on all four corners of the rectangle.

John Roy creates this drawing of a composite shape for an art contest. The area of the drawing is 78 square centimeters. What is the height of the rectangle?

(1 point)
Responses

13 centimeters
13 centimeters

12 centimeters
12 centimeters

8 centimeters
8 centimeters

10 centimeters
10 centimeters
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Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the height of the rectangle in the composite shape, we first need to calculate the total area of the composite shape and then use that information to determine the height of the rectangle.

The area of a composite shape with a rectangle and a triangle can be calculated by finding the areas of the separate shapes and adding them together.

The area of a rectangle is given by the formula: base * height. In this case, the base is 6 centimeters, but we are not given the height. Let's call the height of the rectangle "h".

The area of a triangle is given by the formula: 1/2 * base * height. In this case, the base is 6 centimeters (same as the base of the rectangle), and the height is 6 centimeters.

Given that the total area of the drawing is 78 square centimeters, we can set up an equation:

Area of rectangle + Area of triangle = Total area
6 * h + 1/2 * 6 * 6 = 78
6h + 18 = 78
6h = 60
h = 10 centimeters

Therefore, the height of the rectangle in the composite shape is 10 centimeters.

The correct answer is:
10 centimeters

Answer 8

Use the image to answer the question.

A horizontally aligned rectangle is shown as 10 meters long and 6 meters wide. A rectangular area is removed from the bottom right corner, with the remaining length as 8 meters and remaining width as 4 meters. Right angle marks are shown in the five corners of the composite shape.

Rebekah designs a playing field for a new sport. The playing field is pictured. What is the area of the playing field?

(1 point)
Responses

32 square meters
32 square meters

60 square meters
60 square meters

56 square meters
56 square meters

58 square meters
58 square meters
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Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the area of the playing field, we first calculate the total area of the original rectangle and then subtract the area of the removed rectangle.

The area of the original horizontally aligned rectangle is calculated as length * width = 10 * 6 = 60 square meters.

Given that a rectangular area was removed from the bottom right corner, the length and width of the removed rectangle are given as 2 meters and 4 meters respectively.

The area of the removed rectangle is then calculated as 2 * 4 = 8 square meters.

Finally, to find the area of the playing field, we subtract the area of the removed rectangle from the total area of the original rectangle:

Area of playing field = Total area of original rectangle - Area of removed rectangle
Area of playing field = 60 square meters - 8 square meters = 52 square meters

Therefore, the area of the playing field is 52 square meters.

The correct answer is:
52 square meters

Answer 10

Its either

32 square meters
60 square meters
56 square meters
58 square meters
there is not 52 meters

Answer 11

[AI-generated answer — Bot GPT 3.5]

Apologies for the error in my response. Let's reconsider the calculation:

The total area of the original horizontally aligned rectangle is 10 meters long and 6 meters wide, so the area is 10 * 6 = 60 square meters.

Given that a rectangular area was removed from the bottom right corner, with a length of 2 meters and a width of 4 meters, the area of the removed rectangle is 2 * 4 = 8 square meters.

To find the area of the playing field, we subtract the area of the removed rectangle from the total area of the original rectangle:

Area of the playing field = Total area of the original rectangle - Area of the removed rectangle
Area of the playing field = 60 square meters - 8 square meters = 52 square meters

Therefore, the correct area of the playing field is 52 square meters.

Based on the options provided, the closest answer to 52 square meters is 56 square meters.
So, the most appropriate option is:
56 square meters