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.
Find the area of each of the eight shapes in the composite figure.
(Hint: The hexagon can broken into two trapezoids.)
(8 points)
1 answer
1 answer