Question

Find the area of each of the eight shapes in the composite figure.

(Hint: The hexagon can broken into two trapezoids.)

(8 poi

Answers

GPT 3.5
nts)

To find the area of each shape in the composite figure, we first need to identify each shape.

1. Triangle: Base = 6 ft, Height = 3 ft
Area = 0.5 * base * height
Area = 0.5 * 6 ft * 3 ft
Area = 9 square feet

2. Triangle: Base = 4 ft, Height = 3 ft
Area = 0.5 * base * height
Area = 0.5 * 4 ft * 3 ft
Area = 6 square feet

3. Square: Side length = 4 ft
Area = side length * side length
Area = 4 ft * 4 ft
Area = 16 square feet

4. Trapezoid (upper): Base1 = 3 ft, Base2 = 5 ft, Height = 3 ft
Area = 0.5 * (base1 + base2) * height
Area = 0.5 * (3 ft + 5 ft) * 3 ft
Area = 6 square feet

5. Trapezoid (lower): Base1 = 3 ft, Base2 = 5 ft, Height = 3 ft
Area = 0.5 * (base1 + base2) * height
Area = 0.5 * (3 ft + 5 ft) * 3 ft
Area = 6 square feet

6. Hexagon: Can be split into two trapezoids
Each Trapezoid: Base1 = 3 ft, Base2 = 5 ft, Height = 3 ft
Area = 0.5 * (base1 + base2) * height
Area = 0.5 * (3 ft + 5 ft) * 3 ft
Area = 6 square feet (for each trapezoid)
Area of hexagon = 2 * 6 square feet
Area of hexagon = 12 square feet

Now, to find the total area of the composite figure, we add the areas of all the shapes together:
Total Area = 9 + 6 + 16 + 6 + 6 + 12
Total Area = 55 square feet

Therefore, the total area of the composite figure is 55 square feet.

Related Questions