To calculate the area of the rocket, we need to know the shape of the polygons Sammi used to sketch it. Assuming the rocket is approximated by a triangle (for the body) and a trapezoid (for the cone at the top), we can calculate the area by finding the areas of these shapes and adding them together.
Let's denote the width of the rocket at its widest point as "w = 8 cm," and let's assume the length of the rocket (the vertical height) is "h."
1. Area of the triangle (body):
The area of a triangle is given by the formula:
Area_triangle = 1/2 * base * height
Since the base of the triangle is the width of the rocket (w) and the height is its vertical height (h), the area of the triangle is:
Area_triangle = 1/2 * w * h
2. Area of the trapezoid (cone):
The area of a trapezoid is given by the formula:
Area_trapezoid = 1/2 * (sum of parallel sides) * height
In this case, the sum of the parallel sides is w (since the top of the cone matches the width of the rocket), and the height is some portion of h. Let's denote this portion as "1/3h" since the cone typically takes up about one-third of the rocket's height.
Area_trapezoid = 1/2 * (w + w) * 1/3h = 1/3 * w * h
Now, we sum up the areas of the triangle and the trapezoid:
Total Area = Area_triangle + Area_trapezoid
Total Area = 1/2 * w * h + 1/3 * w * h
Total Area = 5/6 * w * h
Substituting w = 8 cm, we get:
Total Area = 5/6 * 8 * h
Total Area = 40/3 * h
So, the area of the rocket is 40/3 * h square centimeters.
