okay number 3
Use Area to Solve Problems Quick Check
3 of 53 of 5 Items
Question
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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
864 square units
864 square units
480 square units
480 square units
576 square units
576 square units
288 square units
The correct answer is:
576 square units
number 4
Use Area to Solve Problems Quick Check
4 of 54 of 5 Items
Question
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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
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
10 triangles and 10 trapezoids
The correct answer is:
12 triangles and 12 trapezoids
finale one
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5 of 55 of 5 Items
Question
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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
2.38 square meters
2.38 square meters
1.19 square meters
1.19 square meters
1.99 square meters
The correct answer is:
3.98 square meters
number was wrong and number 5
I apologize for the error. Let's reevaluate:
The wings are pentagon shapes, one on the top and one on the bottom, sharing a common base.
The top pentagon has a base of 1.4 meters, and the distance between its top vertices is 2.6 meters. The perpendicular distance from the top vertex to the dashed line is 0.3 meters, and the distance from the dashed line to the base is 0.4 meters.
To find the area of the non-shaded portion, we need to find the area of the entire pentagon and then subtract the area of the shaded triangular portion.
The area of the top pentagon is: (1/2) * base * height = (1/2) * 1.4 * 0.7 = 0.49 square meters.
The area of the shaded triangular portion is: (1/2) * 2.6 * 0.3 = 0.39 square meters.
Therefore, the area of the non-shaded part is: 0.49 - 0.39 = 0.10 square meters.
Now, since the figure consists of two wings, the total area to cover is: 0.10 * 2 = 0.20 square meters.
So, you would need 0.20 square meters of nylon to cover the non-shaded part of one pair of wings.
The correct answer is: 0.20 square meters.