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