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
34 square inches
34 square inches
28 square inches
28 square inches
7 square inches
To find the area of the rectangle within the composite shape, we need to subtract the area of the two congruent right triangles from the total area of the composite shape.
The area of each right triangle is (1/2) * base * height = (1/2) * 3 * 4 = 6 square inches.
Since there are two congruent triangles, the total area of the triangles is 2 * 6 = 12 square inches.
Given that the total area of the composite shape is 40 square inches, the area of the rectangle within the composite shape is 40 - 12 = 28 square inches.
Therefore, the correct answer is 28 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
30 square yards
30 square yards
44 square yards
To find the area of the swimming pool, we need to subtract the area of the rectangle that has been removed from the original rectangle.
The original rectangle has dimensions of 8 yards by 7 yards, so its area is 8 * 7 = 56 square yards.
The rectangle that has been removed has a width of 3 yards. To find the length of the removed rectangle, we can subtract the remaining width of 3 yards from the original width of 7 yards, giving us a length of 7 - 3 = 4 yards.
The area of the removed rectangle is then 3 * 4 = 12 square yards.
To find the area of the swimming pool, we subtract the area of the removed rectangle from the area of the original rectangle: 56 - 12 = 44 square yards.
Therefore, the correct answer 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
13 centimeters
13 centimeters
10 centimeters
10 centimeters
12 centimeters
12 centimeters
8 centimeters
To find the height of the rectangle, we need to divide the area of the composite shape by the base length of the rectangle.
Given that the area of the composite shape is 78 square centimeters and the base length of the rectangle is 6 centimeters, we can set up the equation:
Area = base * height
78 = 6 * height
Dividing both sides of the equation by 6, we find:
height = 78/6 = 13 centimeters
Therefore, the height of the rectangle is 13 centimeters.
Therefore, the correct answer is 13 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
56 square meters
56 square meters
60 square meters
60 square meters
32 square meters
32 square meters
58 square meters
To find the area of the playing field, we need to subtract the area of the rectangle that has been removed from the original rectangle.
The original rectangle has dimensions of 10 meters by 6 meters, so its area is 10 * 6 = 60 square meters.
The rectangle that has been removed has a length of 2 meters and a width of 2 meters. The area of this rectangle is then 2 * 2 = 4 square meters.
To find the area of the playing field, we subtract the area of the removed rectangle from the area of the original rectangle: 60 - 4 = 56 square meters.
Therefore, the correct answer is 56 square meters.