Use the image to answer the question.
An illustration shows a trapezoid with shorter base of length 36 and the opposite longer side of length 48. The legs on the left and right sides are of length 21. The perpendicular height from the bottom left vertex to the longer side is 18. The length between the top left vertex of the longer side and the point where the height meets the longer side is labeled 6. The height is shown in a dashed line.
Compose a rectangle to help find the area of a trapezoid-shaped tabletop in square inches. What is the area of the tabletop?
(1 point)
Responses
882 square inches
882 square inches
648 square inches
648 square inches
864 square inches
864 square inches
756 square inches
756 square inches
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Use the image to answer the question.
An illustration shows a parallelogram that is divided into four equal sections by a horizontal and a vertical line intersecting at the center. Measurements are labeled on the bottom first section as follows: The base is labeled 8 inches and left side is 5 inches. The perpendicular height from the top left vertex to the base is 4 inches. The height is drawn in dashed line.
To cover a garden path, a landscape designer plans to cover a walkway with parallelogram-shaped paving stones. Construct a rectangle to find the area covered by 4 paving stones. What is the area in square inches?
(1 point)
Responses
52 square inches
52 square inches
128 square inches
128 square inches
40 square inches
40 square inches
160 square inches
160 square inches
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3 of 53 of 5 Items
Question
Use the image to answer the question.
An illustration shows two concentric rectangles, an outer and an inner rectangle. The length of the outer rectangle shown vertically is labeled as 36. The width labeled horizontally is 24. The distance between the lengths of the outer and inner rectangle is labeled as 4 on the left and right. The distance between the widths of the outer and inner rectangle is labeled as 6 on the top and bottom. The distances are shown using dashed lines.
A picture framer is painting the front of a picture frame. What is the area of the frame? Assume that all segments that look congruent are congruent and all angles that look like right angles are right angles.
(1 point)
Responses
576 square units
576 square units
288 square units
288 square units
480 square units
480 square units
864 square units
pick an answer
Use the image to answer the question.
An illustration shows a magnified, labeled figure of a two-part wing. The magnified two-part wing shows two similar pentagons, stacked in opposite directions upon each other, sharing a common base. The description of the top pentagon is as follows: The base is 1.4 meters, the bottom left, and right sides are smaller, and the top left and right sides are longer. A dashed line joining the top left and right vertices is labeled as 2.6 meters. The triangular region above this dashed line is shaded. The perpendicular distance from the top vertex to the dashed line is 0.3 meters, and from the dashed line to the base is 0.4 meters.
You are making a dragonfly kite. You want to cover the non-shaded area of the wings with shiny nylon. The dimensions of one pair of wings are shown. Decompose the figure into simple shapes. How many square meters of nylon will you need to cover the non-shaded area of one pair of wings?
(1 point)
Responses
3.98 square meters
3.98 square meters
1.19 square meters
1.19 square meters
2.38 square meters
2.38 square meters
1.99 square meters
1.99 square meters
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To find the area of the trapezoid-shaped tabletop, we can start by constructing a rectangle using the height of 18 inches and the length of the top side of the trapezoid which is 48 inches.
The rectangle would have a length of 18 inches and a width of 48 inches, so the area of the rectangle would be:
Area = Length x Width
Area = 18 inches x 48 inches
Area = 864 square inches
Therefore, the area of the trapezoid-shaped tabletop is 864 square inches.
To find the total area covered by 4 paving stones in the shape of the given parallelogram, we can create a rectangle using the measurements provided.
The base of the parallelogram is 8 inches, and the left side is 5 inches. The height of the parallelogram is 4 inches.
Constructing a rectangle with a base of 8 inches and a height of 4 inches:
Area = Base x Height
Area = 8 inches x 4 inches
Area = 32 square inches
Since 4 paving stones make up the parallelogram, the total area covered by the 4 paving stones would be:
Total Area = 4 x 32 square inches
Total Area = 128 square inches
Therefore, the area covered by 4 paving stones in the shape of the parallelogram is 128 square inches.
To find the area of the frame formed by the two concentric rectangles, we can subtract the area of the inner rectangle from the area of the outer rectangle.
The outer rectangle has a length of 36 units and a width of 24 units. The inner rectangle is formed by reducing the length by 4 units and the width by 6 units.
Calculating the area of the outer rectangle:
Area_outer = Length x Width
Area_outer = 36 units x 24 units
Area_outer = 864 square units
Calculating the area of the inner rectangle:
Length_inner = 36 - 4 = 32 units
Width_inner = 24 - 6 = 18 units
Area_inner = Length_inner x Width_inner
Area_inner = 32 units x 18 units
Area_inner = 576 square units
Therefore, the area of the frame is:
Area_frame = Area_outer - Area_inner
Area_frame = 864 square units - 576 square units
Area_frame = 288 square units
The area of the frame is 288 square units.
Use the image to answer the question.
An illustration shows a composite figure of two similar sets where a central pentagon is surrounded by a layer of 5 pentagons, one on each side. Two central pentagons are drawn separately with dashed lines. On each side of the central pentagons, another pentagon is drawn using solid lines. Each central pentagon has 5 surrounding pentagons. One pentagon from each set shares a common side.
A net that folds into a dodecahedron is made up of pentagons. If you decompose each pentagon into one triangle and one trapezoid, how many triangles and how many trapezoids are there?
(1 point)
Responses
10 triangles and 10 trapezoids
10 triangles and 10 trapezoids
60 triangles and 0 trapezoids
60 triangles and 0 trapezoids
6 triangles and 6 trapezoids
6 triangles and 6 trapezoids
12 triangles and 12 trapezoids
12 triangles and 12 trapezoids
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To determine the number of triangles and trapezoids when each pentagon is decomposed into one triangle and one trapezoid, we can consider that a pentagon has 5 sides, so when split into one triangle and one trapezoid, it results in 5 triangles and 5 trapezoids.
Since we have multiple pentagons in the composite figure, with each pentagon being decomposed into one triangle and one trapezoid, we can multiply the number of triangles and trapezoids obtained from one pentagon by the total number of pentagons.
5 triangles x 5 pentagons = 25 triangles
5 trapezoids x 5 pentagons = 25 trapezoids
Therefore, when each pentagon is decomposed into one triangle and one trapezoid, there will be 25 triangles and 25 trapezoids in total.
The closest response option is 12 triangles and 12 trapezoids, but the correct answer is 25 triangles and 25 trapezoids.