To decompose the figure into simple shapes, we can divide the non-shaded area into a trapezoid and two right triangles.
The trapezoid has a base of 1.4 meters, a longer side length of 2.6 meters, and a shorter side length of 2.4 meters (since 1.4 + 0.3 + 0.4 = 2.1, and 2.6 - 2.1 = 0.5, which is divided equally on both sides).
Calculating the area of the trapezoid:
A = (1/2) * (b1 + b2) * h
A = (1/2) * (1.4 + 2.6) * 0.4
A = (1/2) * 4 * 0.4
A = 0.8 square meters
The two right triangles each have a base of 0.4 meters and a height of 0.3 meters.
Calculating the area of both triangles:
A = (1/2) * b * h
A = (1/2) * 0.4 * 0.3
A = 0.06 square meters
Adding the area of the trapezoid and the two triangles together:
0.8 (trapezoid) + 0.06 (triangle 1) + 0.06 (triangle 2) = 0.92 square meters
Therefore, you will need 0.92 square meters of nylon to cover the non-shaded area of one pair of wings.
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
3.98 square meters
3.98 square meters
1.19 square meters
1.19 square meters
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1 answer
1 answer