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
2.38 square meters
2.38 square meters
1.99 square meters
1.99 square meters
1.19 square meters
1.19 square meters
3.98 square meters
3.98 square meters
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To cover the non-shaded area of one pair of wings with shiny nylon, we can decompose the figure into a trapezoid and two right triangles.
The trapezoid has a base of 1.4 meters, height of 0.4 meters, and top side length of 2.6 meters.
The area of a trapezoid is calculated as: (1/2) * (sum of parallel sides) * height.
A = (1/2) * (1.4 + 2.6) * 0.4
A = (1/2) * 4 * 0.4
A = 0.8 square meters
Each right triangle has a base of 1.4 meters and height of 0.3 meters.
The area of a triangle is calculated as: (1/2) * base * height.
A = (1/2) * 1.4 * 0.3
A = 0.21 square meters (for one triangle)
Since there are two similar right triangles, the total area covered by both triangles is 0.42 square meters.
Therefore, the total area of the non-shaded area of one pair of wings is:
0.8 (trapezoid) + 0.42 (two triangles) = 1.22 square meters
The correct answer is:
1.19 square meters.