se 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
3.98 square meters
3.98 square meters
2.38 square meters
2.38 square meters
1.99 square meters
1.99 square meters
1.19 square meters
To calculate the area of the non-shaded part of one pair of wings, we first need to find the area of the entire figure and then subtract the area of the shaded region.
The entire figure can be decomposed into a rectangle and two right triangles. The dimensions of the rectangle are 1.4 meters (base) and 0.3 meters (height). The dimensions of the two right triangles are 0.5 meters (base) and 0.4 meters (height).
Area of rectangle = base x height = 1.4 x 0.3 = 0.42 square meters
Area of one triangle = 0.5 x 0.4 / 2 = 0.1 square meters (but there are two triangles, so total area for both triangles is 0.1 x 2 = 0.2 square meters)
Total area of the entire figure = 0.42 (rectangle) + 0.2 (triangles) = 0.62 square meters
Now, we need to calculate the area of the shaded region in order to subtract it from the total area.
The shaded region is a triangle with base 1.4 meters and height 0.4 meters. Half of this triangle is shaded.
Area of shaded region = 1.4 x 0.4 / 2 = 0.28 square meters
Area of the non-shaded part of one pair of wings = Total area of the entire figure - Area of shaded region
Area of non-shaded part = 0.62 - 0.28 = 0.34 square meters
Since there are two pairs of wings in total for the dragonfly kite, the total area needed for both pairs of wings is:
0.34 x 2 = 0.68 square meters
Therefore, the correct answer is:
0.68 square meters