Find the area of each of the eight shapes in the composite figure.
(Hint: The hexagon can broken into two trapezoids.)
(8 points)
The area of each shape is as follows:
1. Triangle = 1/2 * base * height = 1/2 * 4 * 5 = 10 square units
2. Rectangle = length * width = 4 * 3 = 12 square units
3. Trapezoid 1 = 1/2 * (base1 + base2) * height = 1/2 * (6 + 4) * 3 = 7.5 square units
4. Trapezoid 2 = 1/2 * (base1 + base2) * height = 1/2 * (6 + 2) * 3 = 12 square units
5. Hexagon (both trapezoids together) = Trapezoid 1 + Trapezoid 2 = 7.5 + 12 = 19.5 square units
6. Triangle = 1/2 * base * height = 1/2 * 4 * 3 = 6 square units
7. Square = side^2 = 2^2 = 4 square units
8. Triangle = 1/2 * base * height = 1/2 * 2 * 3 = 3 square units
Therefore, the area of each shape in the composite figure is:
1. 10 square units
2. 12 square units
3. 7.5 square units
4. 12 square units
5. 19.5 square units
6. 6 square units
7. 4 square units
8. 3 square units