Calculate the total area of the figure you designed. Show your work. Include the
correct units for area in your answer.
Describe in words how you calculated the area of each shape. Be sure to include
which formulas you used. For which polygon(s) did you compose a rectangle to find
the area? Which polygon(s) did you decompose into simpler shapes? Which simple
shapes did you use? Triangle hexagon square
To calculate the total area of the figure I designed, I divided it into three basic shapes: a triangle, a hexagon, and a square.
1. Triangle:
I used the formula for the area of a triangle, which is Area = 0.5 * base * height.
In this case, the base of the triangle is 8 units and the height is 4 units, so the area of the triangle is:
Area = 0.5 * 8 * 4 = 16 square units.
2. Hexagon:
To find the area of the hexagon, I decomposed it into 6 equilateral triangles.
Each side of the hexagon is 4 units, so the base of each triangle is 4 units. The height can be found using the Pythagorean theorem, which gives us a height of √(4^2 - 2^2) = √12 ≈ 3.46 units.
The area of one triangle is then 0.5 * 4 * 3.46 = 6.92 square units.
Since there are 6 triangles in the hexagon, the total area of the hexagon is 6 * 6.92 = 41.52 square units.
3. Square:
The area of a square is calculated using the formula Area = side * side.
In this case, the side length of the square is 4 units, so the area of the square is:
Area = 4 * 4 = 16 square units.
Total Area:
To find the total area of the entire figure, I added the areas of the triangle, hexagon, and square together:
Total Area = 16 + 41.52 + 16 = 73.52 square units.
Therefore, the total area of the figure is 73.52 square units.