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?
To decompose the figure into simple shapes, we can divide it into two triangles and two trapezoids.
First, we can calculate the area of the two triangles:
Area of triangle 1 = (0.5 * base * height) = 0.5 * 1.4 * 0.3 = 0.21 square meters
Area of triangle 2 = (0.5 * base * height) = 0.5 * 1.4 * 0.4 = 0.28 square meters
Next, we can calculate the area of the two trapezoids:
Area of trapezoid 1 = 0.5 * (0.3 + 0.4) * 2.6 = 0.845 square meters
Area of trapezoid 2 = 0.5 * (0.3 + 0.4) * 0.4 = 0.175 square meters
Add the areas of all shapes together:
Total area = 0.21 + 0.28 + 0.845 + 0.175 = 1.5 square meters
You will need 1.5 square meters of nylon to cover the non-shaded area of one pair of wings.