Find the area of each of the eight shapes in the composite figure.
(Hint: The hexagon can broken into two trapezoids.)
(8 points)
To find the area of each shape in the composite figure, we need to calculate the areas of each individual shape and then add them up.
1. Rectangle:
Area = length x width
Area = 6 x 4
Area = 24 square units
2. Triangle:
Area = 1/2 x base x height
Area = 1/2 x 3 x 4
Area = 6 square units
3. Trapezoid:
Area = 1/2 x (base1 + base2) x height
Area = 1/2 x (4 + 4) x 3
Area = 1/2 x 8 x 3
Area = 12 square units
4. Hexagon (broken into two trapezoids):
Each trapezoid's area = 1/2 x (base1 + base2) x height
Area of each trapezoid = 1/2 x (3 + 3) x 4
Area of each trapezoid = 1/2 x 6 x 4
Area of each trapezoid = 12 square units
Now, we add up the areas of all shapes:
Rectangle = 24 square units
Triangle = 6 square units
Trapezoid = 12 square units
Hexagon (both trapezoids) = 12 + 12 = 24 square units
Total area of the composite figure = 24 + 6 + 12 + 24 = 66 square units
Therefore, the total area of the composite figure is 66 square units.