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 cover the non-shaded area of the wings with shiny nylon, we can decompose the figure into simple shapes, such as triangles and rectangles.
First, we can see that the non-shaded area of one wing consists of two triangles and one rectangle. We can calculate the area of each shape separately and then add them up to get the total area of the non-shaded area of one wing.
Let's label the dimensions of the shapes:
- The base of the large triangle is 10 cm and the height is 11 cm.
- The base of the small triangle is 5 cm and the height is also 5 cm.
- The width of the rectangle is 5 cm and the height is 11 cm.
Now, we can calculate the area of each shape:
- Area of the large triangle = (1/2) * base * height = (1/2) * 10 cm * 11 cm = 55 cm^2
- Area of the small triangle = (1/2) * base * height = (1/2) * 5 cm * 5 cm = 12.5 cm^2
- Area of the rectangle = base * height = 5 cm * 11 cm = 55 cm^2
Total area of the non-shaded area of one wing = 55 cm^2 + 12.5 cm^2 + 55 cm^2 = 122.5 cm^2
To convert this area into square meters, we need to divide by 10,000 (since 1 m^2 = 10,000 cm^2):
122.5 cm^2 รท 10,000 = 0.01225 m^2
Therefore, you will need 0.01225 square meters of shiny nylon to cover the non-shaded area of one pair of wings.