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
1.19 square meters
1.19 square meters
1.99 square meters
1.99 square meters
3.98 square meters
3.98 square meters
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To find the area of the non-shaded area of one pair of wings, we need to first decompose the figure into simple shapes. We can split the figure into two triangles and a rectangle.
The two triangles have base and height dimensions of 1.4 meters and 0.3 meters, as well as 0.4 meters and 2.6 meters. To find the area of a triangle, we use the formula: (1/2) * base * height.
Area of the first triangle = (1/2) * 1.4 * 0.3 = 0.21 square meters
Area of the second triangle = (1/2) * 2.6 * 0.4 = 0.52 square meters
Next, we calculate the area of the rectangle. The base of the rectangle is 1.4 meters and the height is 0.4 meters. To find the area of a rectangle, we use the formula: base * height.
Area of the rectangle = 1.4 * 0.4 = 0.56 square meters
Finally, we add the areas of the two triangles and the rectangle to find the total area of the non-shaded area of one pair of wings:
Total area = 0.21 + 0.52 + 0.56 = 1.29 square meters
Therefore, you will need 1.29 square meters of nylon to cover the non-shaded area of one pair of wings. The closest answer option is 1.19 square meters.