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.

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

Answer 1

To calculate the area of the non-shaded area of the wings, we need to decompose the figure into simple shapes. In this case, we have a trapezoid and two triangles.

The trapezoid can be divided into a rectangle and two right triangles. The rectangle has a base of 1.4 meters and a height of 0.4 meters. Therefore, the area of the rectangle is 1.4m * 0.4m = 0.56 square meters.

Each right triangle has a base of 0.7 meters (half of 1.4m) and a height of 0.3 meters. So the area of one right triangle is 0.5 * 0.7m * 0.3m = 0.105 square meters. Since there are two right triangles, the total area of both right triangles is 2 * 0.105 square meters = 0.21 square meters.

Now we move on to the two triangles outside the trapezoid. Each of these triangles has a base of 1.4 meters and a height of 0.3 meters. Therefore, the area of each triangle is 0.5 * 1.4m * 0.3m = 0.21 square meters. Since there are two such triangles, the total area of both triangles is 2 * 0.21 square meters = 0.42 square meters.

Adding up the areas of the rectangle, two right triangles, and two triangles outside the trapezoid, we get a total of 0.56 square meters + 0.21 square meters + 0.42 square meters = 1.19 square meters.

Therefore, you will need 1.19 square meters of nylon to cover the non-shaded area of one pair of wings.

So, the correct response is:

1.19 square meters