A net that folds into a dodecahedron is made up of pentagons. If you decompose each pentagon into one triangle and one trapezoid, how many triangles and how many trapezoids are there?
2 flowers made of pentagons
Answers: 10 triangles and 10 Trapezoids
60 triangles and 0 trapezoids
6 triangles and 0 trapezoids
12 triangles and 12 trapezoids
10 triangles and 10 trapezoids
You are making a dragonfly kite. You want to cover the non-shades 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-shades area of one pair of wings?
0.3 m —
0.4 m. :
:
—
2.6 m width 1.4 meter middle width
To decompose the shape into simpler shapes, we can split the wings into a trapezoid and a triangle as shown:
1. Trapezoid Wing:
Base 1 = 0.3 m
Base 2 = 2.6 m
Height = 1.4 m
Area of Trapezoid = 1/2 x (Base 1 + Base 2) x Height
Area = 1/2 x (0.3 + 2.6) x 1.4
Area = 1/2 x 2.9 x 1.4 = 2.03 square meters
2. Triangle Wing:
Base = 2.6 m
Height = 0.4 m
Area of Triangle = 1/2 x Base x Height
Area = 1/2 x 2.6 x 0.4 = 0.52 square meters
Therefore, the total area that needs to be covered by shiny nylon on one pair of wings is:
Total Area = Area of Trapezoid + Area of Triangle
Total Area = 2.03 + 0.52 = 2.55 square meters
You will need 2.55 square meters of nylon to cover the non-shaded area of one pair of wings of the dragonfly kite.