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