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
28 square inches
34 square inches
16 square inches
7 square inches
The area of the triangle is 1/2 * base * height = 1/2 * 3 * 4 = 6 square inches for each triangle. Since there are two triangles, the total area for both triangles is 6 * 2 = 12 square inches.
The total area of the composite figure is 40 square inches. Therefore, the area of the rectangle can be found by subtracting the area of the triangles from the total area: 40 - 12 = 28 square inches.
Therefore, the area of the rectangle within the composite shape is 28 square inches.
Correct answer: 28 square inches
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
56 square yards
30 square yards
44 square yards
To find the area of the swimming pool, we need to first find the area of the original vertically aligned rectangle, and then subtract the area of the rectangle that was removed.
Area of the original vertically aligned rectangle = length * width = 8 yards * 7 yards = 56 square yards.
The horizontally aligned rectangle that was removed has a width of 3 yards and an unknown length. Since the remaining width is also 3 yards, we can calculate the length of the rectangle that was removed by subtracting it from the total original width:
7 yards (original width) - 3 yards (remaining width) = 4 yards.
Now, we can find the area of the rectangle that was removed:
Area of the removed rectangle = length * width = 4 yards * 3 yards = 12 square yards.
Finally, we can find the area of the swimming pool by subtracting the area of the rectangle that was removed from the area of the original rectangle:
56 square yards (original area) - 12 square yards (removed rectangle area) = 44 square yards.
Therefore, the area of the swimming pool in square yards is 44 square yards.
Correct answer: 44 square yards.
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
12 centimeters
13 centimeters
8 centimeters
To find the height of the rectangle, we need to first calculate the area of the rectangle and the area of the triangle, and then add them together to get the total area of the composite shape. Since the height of the triangle is given as 6 centimeters, we can find the base of the triangle by halving the base of the rectangle, since they share a common side.
Area of the rectangle = base * height = 6 cm * h cm = 6h square cm.
Area of the triangle = 1/2 * base * height = 1/2 * 6 cm * 6 cm = 18 square cm.
Total area of the composite shape = Area of rectangle + Area of triangle = 6h + 18 = 78 square cm.
Now we solve for h:
6h + 18 = 78
6h = 60
h = 10 cm
Therefore, the height of the rectangle is 10 centimeters.
Correct answer: 10 centimeters.
An illustration shows a shape that appears as a square with a semicircle attached on the left side and the top. The side of the square is 2 inches and the diameter of the semicircles is 2 inches. The overlapping lines, which include the top and left side of the square, are marked as dashed lines. Right angle symbols are shown on the top left and bottom right corners of the square.
You are making a card for a friend that looks like a heart shape. Solve for the total area of the shape. Use 3.14 as pi. Round the answer to the nearest hundredth.
(1 point)
Responses
10.28 in.2
10.28 in. squared
16.56 in.2
16.56 in. squared
7.14 in.2
7.14 in. squared
5.57 in.2
5.57 in. squared
To find the total area of the shape, we need to find the areas of the square and the two semicircles, and then subtract the overlapping region where they intersect.
Area of the square = side * side = 2 inches * 2 inches = 4 square inches.
Area of one semicircle = 1/2 * pi * radius^2 = 1/2 * 3.14 * (2/2)^2 = 1.57 square inches.
Area of two semicircles = 1.57 square inches + 1.57 square inches = 3.14 square inches.
The overlapping region where the semicircles intersect forms a square with side equal to the radius of the semicircle (2/2 = 1 inch).
Area of overlapping square = 1 inch * 1 inch = 1 square inch.
Total area = Area of square + Area of two semicircles - Area of overlapping square = 4 square inches + 3.14 square inches - 1 square inch = 6.14 square inches.
Rounded to the nearest hundredth, the total area of the shape is 6.14 in^2.
Correct answer: 6.14 in.²