Use the image to answer the question.

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

1.19 square meters
1.19 square meters

2.38 square meters
2.38 square meters

1.99 square meters

Answer 1

To find the total area of the non-shaded area of the two wings, we can decompose the figure into simple shapes.

We can see that the non-shaded area can be divided into two trapezoids (one on each side of the wing) and two right triangles.

First trapezoid:
Base 1 = 1.4 meters
Base 2 = 1.2 meters (calculated by subtracting 0.2 meters from 1.4 meters)
Height = 0.3 meters
Area of this trapezoid = 0.5 * (Base 1 + Base 2) * Height = 0.5 * (1.4 + 1.2) * 0.3 = 0.39 square meters

Second trapezoid:
Base 1 = 1.4 meters
Base 2 = 1.2 meters (calculated by subtracting 0.2 meters from 1.4 meters)
Height = 0.4 meters
Area of this trapezoid = 0.5 * (Base 1 + Base 2) * Height = 0.5 * (1.4 + 1.2) * 0.4 = 0.56 square meters

First right triangle:
Base = 0.2 meters
Height = 0.3 meters
Area of this triangle = 0.5 * Base * Height = 0.5 * 0.2 * 0.3 = 0.03 square meters

Second right triangle:
Base = 0.2 meters
Height = 0.4 meters
Area of this triangle = 0.5 * Base * Height = 0.5 * 0.2 * 0.4 = 0.04 square meters

Total area of the non-shaded part of one pair of wings = 0.39 + 0.56 + 0.03 + 0.04 = 1.02 square meters

Therefore, you will need 1.02 square meters of nylon to cover the non-shaded area of one pair of wings.

So the closest option is: 1.19 square meters.