To find the area of each shape in the composite figure, we can break it down into simpler shapes and then find the area of each individual shape.
1. Rectangle A:
Area = length x width
Area = 8 x 4
Area = 32 square units
2. Triangle B:
Area = (1/2) x base x height
Area = (1/2) x 6 x 3
Area = 9 square units
3. Trapezoid 1:
We can find the area of Trapezoid 1 by breaking it down into a rectangle and a triangle.
Area of rectangle = length x width = 3 x 2 = 6 square units
Area of triangle = (1/2) x base x height = (1/2) x 1 x 4 = 2 square units
Total area of Trapezoid 1 = Area of rectangle + Area of triangle
Total area = 6 + 2 = 8 square units
4. Trapezoid 2:
Similar to Trapezoid 1, we can find the area of Trapezoid 2 by breaking it down into a rectangle and a triangle.
Area of rectangle = length x width = 3 x 2 = 6 square units
Area of triangle = (1/2) x base x height = (1/2) x 1 x 4 = 2 square units
Total area of Trapezoid 2 = Area of rectangle + Area of triangle
Total area = 6 + 2 = 8 square units
5. Hexagon:
The hexagon can be broken down into two trapezoids. We have already found the area of these trapezoids in steps 3 and 4.
Total area of hexagon = Total area of Trapezoid 1 + Total area of Trapezoid 2
Total area = 8 + 8 = 16 square units
6. Trapezoid 3:
We can find the area of Trapezoid 3 by breaking it down into a rectangle and a triangle.
Area of rectangle = length x width = 8 x 2 = 16 square units
Area of triangle = (1/2) x base x height = (1/2) x 2 x 4 = 4 square units
Total area of Trapezoid 3 = Area of rectangle + Area of triangle
Total area = 16 + 4 = 20 square units
7. Triangle C:
Area = (1/2) x base x height
Area = (1/2) x 4 x 2
Area = 4 square units
8. Rectangle D:
Area = length x width
Area = 6 x 4
Area = 24 square units
Therefore, the area of each shape in the composite figure is as follows:
Rectangle A: 32 sq units
Triangle B: 9 sq units
Trapezoid 1: 8 sq units
Trapezoid 2: 8 sq units
Hexagon: 16 sq units
Trapezoid 3: 20 sq units
Triangle C: 4 sq units
Rectangle D: 24 sq units
Find the area of each of the eight shapes in the composite figure. (Hint: The hexagon can broken into two trapezoids.)
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