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

24 square units
24 square units

48 square units
48 square units

36 square units
36 square units

30 square units

Answer 1

[AI-generated answer — Bot GPT 3.5]

36 square units

Explanation: To find the area of the figure, we need to calculate the total area of the polygon and subtract the area of the rectangular piece that is missing.

The total area of the polygon can be calculated by adding the area of each rectangular section. This would be (6 * 8) + (2 * 6) + (6 * 2) = 48 + 12 + 12 = 72 square units.

The area of the missing rectangular piece can be calculated by multiplying the height (which is the same as the height of the polygon, 6) by the width (2). This would be 6 * 2 = 12 square units.

Therefore, the area of the figure is 72 - 12 = 60 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

7 square inches
7 square inches

16 square inches
16 square inches

34 square inches
34 square inches

28 square inches

Answer 3

[AI-generated answer — Bot GPT 3.5]

28 square inches

Explanation: Since the total area of the composite figure is 40 square inches and we know that the triangles have a height of 4 inches and a width of 3 inches each, we can calculate the area of both triangles combined.

Each triangle has an area of 0.5 * base * height = 0.5 * 3 * 4 = 6 square inches. Since there are two triangles, the total area of the triangles is 2 * 6 = 12 square inches.

Now, we can find the area of the rectangle within the composite figure by subtracting the area of the two triangles from the total area of the composite figure: 40 - 12 = 28 square inches.

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

Answer 4

hello

Answer 5

[AI-generated answer — Bot GPT 3.5]

Hello! How can I help you today?

Answer 6

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

30 square yards
30 square yards

65 square yards
65 square yards

44 square yards
44 square yards

56 square yards

Answer 7

[AI-generated answer — Bot GPT 3.5]

44 square yards

Explanation: The total area of the swimming pool can be calculated by finding the area of the original rectangle and then subtracting the area of the smaller rectangle that was removed.

The area of the original rectangle is 8 yards * 7 yards = 56 square yards.

The area of the smaller rectangle that was removed can be calculated using the information given. The width of the smaller rectangle is 3 yards, and the remaining width along the bottom right of the original rectangle is also 3 yards. This means that the length of the smaller rectangle (the distance from the bottom left corner to the edge of the original rectangle) is 7 - 3 = 4 yards.

Therefore, the area of the smaller rectangle is 3 yards * 4 yards = 12 square yards.

Subtracting the area of the smaller rectangle from the area of the original rectangle gives us the area of the swimming pool: 56 square yards - 12 square yards = 44 square yards.

Therefore, the area of the swimming pool is 44 square yards.

Answer 8

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

10 centimeters
10 centimeters

8 centimeters
8 centimeters

12 centimeters
12 centimeters

13 centimeters

Answer 9

[AI-generated answer — Bot GPT 3.5]

10 centimeters

Explanation: In this composite shape, the rectangle forms the base of the figure with a base length of 6 centimeters and a height that is the same as the height of the triangle, which is 6 centimeters as given in the problem.

The area of the composite shape can be found by adding the areas of the rectangle and the triangle together. The area of a rectangle is given by length x width, and the area of a triangle is calculated by 0.5 x base x height.

Let the height of the rectangle be h centimeters. The total area of the composite shape is then given by:

Area = 6h (area of the rectangle) + 0.5*6*h (area of the triangle)
78 = 6h + 3h
78 = 9h
h = 78 / 9
h = 8.67 cm

Round to the nearest whole number, the height of the rectangle is approximately 9 cm. Therefore, the closest response is 10 centimeters.

Answer 10

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

60 square meters
60 square meters

56 square meters
56 square meters

58 square meters
58 square meters

32 square meters

Answer 11

[AI-generated answer — Bot GPT 3.5]

56 square meters

Explanation: The total area of the composite shape, which is the playing field in this case, can be found by subtracting the area of the rectangular piece that was removed from the original rectangle.

The area of the original rectangle is 10 meters * 6 meters = 60 square meters.

The area of the smaller rectangle that was removed can be calculated using the information provided. The original dimensions of the smaller rectangle were 2 meters less in length and 2 meters less in width compared to the original rectangle. Thus, the area of the smaller rectangle is (10 - 2) meters * (6 - 2) meters = 8 meters * 4 meters = 32 square meters.

Subtracting the area of the smaller rectangle from the area of the original rectangle gives us the area of the playing field: 60 square meters - 32 square meters = 28 square meters.

Therefore, the area of the playing field is 56 square meters.