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. Rectangle: length = 3, width = 2
Area = length x width = 3 x 2 = 6

2. Trapezoid 1: b1 = 3, b2 = 6, height = 2
Area = 1/2 x (b1 + b2) x height = 1/2 x (3 + 6) x 2 = 1/2 x 9 x 2 = 9

3. Trapezoid 2: b1 = 2, b2 = 3, height = 2
Area = 1/2 x (b1 + b2) x height = 1/2 x (2 + 3) x 2 = 1/2 x 5 x 2 = 5

4. Triangle 1: base = 2, height = 2
Area = 1/2 x base x height = 1/2 x 2 x 2 = 2

5. Triangle 2: base = 2, height = 2
Area = 1/2 x base x height = 1/2 x 2 x 2 = 2

6. Hexagon (Trapezoid 3): b1 = 2, b2 = 3, height = 2
Area = 1/2 x (b1 + b2) x height = 1/2 x (2 + 3) x 2 = 1/2 x 5 x 2 = 5

7. Hexagon (Trapezoid 4): b1 = 2, b2 = 3, height = 2
Area = 1/2 x (b1 + b2) x height = 1/2 x (2 + 3) x 2 = 1/2 x 5 x 2 = 5

8. Parallelogram: base = 3, height = 2
Area = base x height = 3 x 2 = 6

Total area of the composite figure = 6 + 9 + 5 + 2 + 2 + 5 + 5 + 6 = 40 square units.