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

A. 1.19 square meters

B. 1.99 square meters

C. 2.38 square meters

D. 3.98 square meters

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

We can see that the non-shaded region is made up of two trapezoids and a triangle.

The area of a trapezoid is given by the formula A = (a + b) * h / 2, where a and b are the lengths of the parallel sides and h is the height.

For the trapezoid above the dashed line:
a = 1.4, b = 2.6, h = 0.3
A = (1.4 + 2.6) * 0.3 / 2 = 1.2 square meters

For the trapezoid below the dashed line:
a = 1.4, b = 2.6, h = 0.4
A = (1.4 + 2.6) * 0.4 / 2 = 1.6 square meters

For the triangle:
base = 1.4, height = 0.3
A = 1.4 * 0.3 / 2 = 0.21 square meters

Adding up the areas of the trapezoids and triangle:
1.2 + 1.6 + 0.21 = 3.01 square meters

Therefore, you will need 3.01 square meters of nylon to cover the non-shaded area of one pair of wings.

D. 3.98 square meters