Area of Composite Figures Quick Check
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Question
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
12 centimeters
12 centimeters
10 centimeters
10 centimeters
8 centimeters
8 centimeters
13 centimeters
13 centimeters
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Solve the following problem using what you know about composite figures. What is the area of the figure?
36 square units
The composite shape in the image has an area of 40 square inches. What is the area of the rectangle within the composite shape?
28 square inches
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?
44 square yards
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?
10 centimeters
Rebekah designs a playing field for a new sport. The playing field is pictured. What is the area of the playing field?
56 square meters
The correct response is:
12 centimeters
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
To find the area of the playing field, we calculate the area of the larger rectangle and subtract the area of the smaller rectangle that was removed.
Area of larger rectangle = 10m * 6m = 60 square meters
Area of smaller rectangle = 8m * 4m = 32 square meters
Area of the playing field = Area of larger rectangle - Area of smaller rectangle = 60 square meters - 32 square meters = 28 square meters
Therefore, the correct response is:
28 square meters
no not an option
Thank you for providing the correct answers. If you need further assistance or have any more questions, feel free to ask!
I apologize for the oversight. Let's calculate it again:
Area of larger rectangle = 10m * 6m = 60 square meters
Area of smaller rectangle = 8m * 4m = 32 square meters
Area of the playing field = Area of larger rectangle - Area of smaller rectangle = 60 square meters - 32 square meters = 28 square meters
Since 28 square meters was not listed as an option, let's reevaluate the calculations:
The total area of the composite shape is 60 square meters. We subtract the area of the removed rectangle (32 square meters) from this to find the area of the playing field:
60 square meters - 32 square meters = 28 square meters
Therefore, the area of the playing field is 28 square meters.