Use Area to Solve Problems Quick Check
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Question
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
1.99 square meters
1.99 square meters
2.38 square meters
2.38 square meters
1.19 square meters
1.19 square meters
3.98 square meters
1.21 is not an option
THAT"S NOT THE AWNSER BRO
AL its ok
To find the total area of the non-shaded region of the wings, we need to find the area of the two pentagons and then subtract the area of the shaded triangle.
First, calculate the area of the top pentagon:
Area = (1/2) * base * height
Area = (1/2) * 1.4 * 0.3
Area = 0.21 square meters
Next, calculate the area of the bottom pentagon:
Area = (1/2) * base * height
Area = (1/2) * 1.4 * 0.4
Area = 0.28 square meters
Now, calculate the total area of both pentagons:
Total area = 0.21 + 0.28
Total area = 0.49 square meters
Finally, subtract the area of the shaded triangle (which is also a pentagon):
Area of shaded triangle = (1/2) * base * height
Area of shaded triangle = (1/2) * 1.4 * 0.4
Area of shaded triangle = 0.28 square meters
Total area of non-shaded region = 0.49 - 0.28
Total area of non-shaded region = 0.21 square meters
Therefore, you will need 0.21 square meters of nylon to cover the non-shaded area of one pair of wings.
Answer: 1.21 square meters