5. Use the image to answer the question.
An illustration shows a wing-like structure with two-part wings on either side, and 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. The base is extended out to the right to the length of the top right vertex using a dashed line, labeled as 0.6 meters. The right vertices on the top and bottom pentagons are joined with a solid line labeled as height 0.8 meters. This line forms a triangle with the right short sides of the pentagons. This triangle is shaded. Adjacent to magnified wing, a winged figure is shown with a long central oval shape with two-part wings extending left and right from two small triangles above the long oval. A small circle sits on top of the figure.
You are making a dragonfly kite. You want to cover all parts of all four wings, including the triangles in the center, with shiny nylon. The dimensions of one pair of wings is shown. The kite will need two sets of wings. Decompose the figure on the left into simple shapes. How many square meters of nylon will you need to cover both pairs of wings?
(1 point)
Responses
5.24 square meters
5.24 square meters
10.48 square meters
10.48 square meters
4.76 square meters
4.76 square meters
2.62 square meters
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answered by ya
The figure can be decomposed into a rectangle, two right triangles, and a trapezoid.
The area of the rectangle is 1.4 meters * 0.8 meters = 1.12 square meters.
The area of each right triangle is 0.5 * base * height.
For the first right triangle, the base is 0.4 meters and the height is 0.8 meters, so the area is 0.5 * 0.4 * 0.8 = 0.16 square meters. Since there are two right triangles, the total area for the right triangles is 0.32 square meters.
The area of the trapezoid is 0.5 * (base1 + base2) * height.
The bases are 0.6 meters and 0.8 meters, and the height is 2.6 meters, so the area is 0.5 * (0.6 + 0.8) * 2.6 = 1.56 square meters.
Adding all the areas together, the total area for both pairs of wings is 1.12 + 0.32 + 1.56 = 2.62 square meters.
Therefore, the correct answer is 2.62 square meters.