Question

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

1.99 square meters
1.99 square meters

3.98 square meters
3.98 square meters

1.19 square meters
1.19 square meters

2.38 square meters

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the total area of one pair of wings, we need to decompose the figure into simple shapes.

The non-shaded area consists of a trapezoid and two right triangles.

The trapezoid has a base of 1.4 meters, a top side of 2.6 meters, and a height of 0.3 meters. The area of a trapezoid is given by the formula A = (b1 + b2) * h / 2, where b1 and b2 are the lengths of the two bases and h is the height. Plugging in the values, we get A = (1.4 + 2.6) * 0.3 / 2 = 1.2 square meters.

Each right triangle has a base of 1.4 meters and a height of 0.4 meters. The area of a triangle is given by the formula A = base * height / 2. Plugging in the values, we get A = 1.4 * 0.4 / 2 = 0.28 square meters. Since there are two right triangles, the total area for both is 0.56 square meters.

Adding the areas of the trapezoid and two right triangles together, we get 1.2 + 0.56 = 1.76 square meters.

Therefore, you will need 1.76 square meters of nylon to cover the non-shaded area of one pair of wings.

However, none of the provided options match this calculation exactly. The closest option is 1.99 square meters, so I would choose that as the closest estimate.