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
3.98 square meters
3.98 square meters
1.19 square meters
1.19 square meters
1.99 square meters
1.99 square meters
Skip to navigation
To find the total area of the non-shaded part of one pair of wings, we can decompose the figure into simple shapes and calculate the area of each shape separately.
1. Area of the larger triangle (top part of the wing):
base = 1.4 meters
height = 0.3 meters
Area = 0.5 * base * height = 0.5 * 1.4 * 0.3 = 0.21 square meters
2. Area of the trapezoid (bottom part of the wing):
b1 = 1.4 meters
b2 = 1.4 + 0.3 = 1.7 meters
h = 0.4 meters
Area = 0.5 * (b1 + b2) * h = 0.5 * (1.4 + 1.7) * 0.4 = 0.94 square meters
Total area = Area of larger triangle + Area of trapezoid = 0.21 + 0.94 = 1.15 square meters
Therefore, you will need 1.15 square meters of shiny nylon to cover the non-shaded area of one pair of wings. The closest answer choice is 1.19 square meters.