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
28 square inches
16 square inches
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
56 square yards
56 square yards
65 square yards
65 square yards
44 square yards
44 square yards
30 square yards
The area of the swimming pool can be calculated as follows:
Area of the original rectangle = 8 yards * 7 yards = 56 square yards
Area of the removed rectangle = 3 yards * 3 yards = 9 square yards
Area of the swimming pool = Area of the original rectangle - Area of the removed rectangle = 56 square yards - 9 square yards = 47 square yards
Therefore, the area of the swimming pool is 47 square yards.
So, the closest answer option is:
44 square yards.
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
13 centimeters
13 centimeters
12 centimeters
12 centimeters
8 centimeters
8 centimeters
To find the height of the rectangle, we can first find the area of the rectangle, which is the base (6 cm) times the height (h) of the rectangle.
Area of rectangle = base * height
Area of rectangle = 6 cm * h
The area of the triangle and the rectangle add up to 78 square centimeters. Since the triangle has a base of 6 cm and a height of 6 cm (as it is vertical and has a base on top of the rectangle), the area of the triangle is (1/2)*6 cm * 6 cm = 18 square centimeters.
So, the area of the rectangle (6 cm * h) + the area of the triangle (18 square cm) = total area of the composite shape (78 square cm):
6h + 18 = 78
6h = 60
h = 10
Therefore, the height of the rectangle is 10 centimeters.
The correct response is:
10 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
32 square meters
32 square meters
58 square meters
58 square meters
56 square meters
56 square meters
60 square meters
To find the area of the playing field, we first calculate the area of the original rectangle and then subtract the area of the smaller rectangle that was removed.
Area of the original rectangle = 10 meters * 6 meters = 60 square meters
Area of the removed rectangle = 8 meters * 4 meters = 32 square meters
Area of the playing field = Area of original rectangle - Area of removed rectangle = 60 square meters - 32 square meters = 28 square meters
Therefore, the area of the playing field is 28 square meters.
The correct response is:
28 square meters