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
plese try again
The figure on the left can be decomposed into a rectangle with dimensions 1.4 meters by 2.6 meters, and two right triangles with base 0.6 meters and height 0.8 meters.
Area of rectangle = length x width = 1.4 meters x 2.6 meters = 3.64 square meters
Area of right triangle = 1/2 x base x height = 1/2 x 0.6 meters x 0.8 meters = 0.24 square meters (for one triangle)
Total area for one pair of wings = 3.64 square meters + 0.24 square meters + 0.24 square meters = 4.12 square meters
Since the kite needs two sets of wings, the total area needed to cover both pairs of wings = 4.12 square meters x 2 = 8.24 square meters
Therefore, you will need 8.24 square meters of shiny nylon to cover both pairs of wings.
Answer: 8.24 square meters
To cover both pairs of wings, you need to calculate the total area of all four wings, including the triangles in the center.
For one pair of wings:
1. Rectangle: 1.4 meters x 2.6 meters = 3.64 square meters
2. Triangles (2): 1/2 x 0.6 meters x 0.8 meters = 0.24 square meters each, so 0.24 square meters x 2 = 0.48 square meters
Total area for one pair of wings = 3.64 square meters + 0.48 square meters = 4.12 square meters
Since the kite needs two sets of wings, the total area needed to cover both pairs of wings = 4.12 square meters x 2 = 8.24 square meters
Therefore, you will need 8.24 square meters of shiny nylon to cover both pairs of wings.
Answer: 8.24 square meters