The formula to calculate the surface area of a triangular prism is:
Surface Area = 2(lw + lh + wh)
Given that the top and bottom are red cardboard, we only need to calculate the surface area of the lateral faces, which are made of white cardboard.
We know that the length of the triangle base (l) is equal to the width of the triangle base (w) as the container is in the shape of an equilateral triangle.
The height of the triangular prism (h) is the height of the triangle base.
Let's assume the side length of the equilateral triangle base is x. Then, the height can be calculated using the Pythagorean theorem as h = x* sqrt(3) / 2.
Now, we can calculate the surface area of the lateral faces:
lateral surface area = 2l * h + l * h = 2(x) * (x * sqrt(3) / 2) + x * (x * sqrt(3) / 2) = x^2 * sqrt(3) + x^2 * sqrt(3) / 2
Since we have two lateral faces on the pizza container, we need to multiply this result by 2:
lateral surface area = 2(x^2 * sqrt(3) + x^2 * sqrt(3) / 2) = 2x^2 * sqrt(3) + x^2 * sqrt(3) = 3x^2 * sqrt(3)
To find the value of x, we need to know the dimensions of the equilateral triangle base. Once we have the side length, we can substitute it into the formula to calculate the amount of white cardboard needed.
Party Pizza Palace has cardboard containers for customers ordering only one slice of pizza to go. The container is made of cardboard and is in the shape of a triangular prism. The top and bottom are made of red cardboard, and the lateral faces are made of white cardboard. How much white cardboard is needed to make one pizza container? 10.8 7.2 1.5 9 9 (1 point)
3 answers
calculate the formula
Given that the top and bottom of the pizza container are red and the lateral faces are white, we need to calculate the surface area of the lateral faces, which are in the shape of an equilateral triangle.
The surface area of an equilateral triangle can be calculated using the formula:
Area = (sqrt(3) / 4) * side length^2
Since each lateral face of the triangular prism is an equilateral triangle, we need to find the side length x of the equilateral triangle base. The height h of the triangle can be calculated as h = x * sqrt(3) / 2.
Now, the lateral surface area of the pizza container can be calculated as:
lateral surface area = 2 * lateral face area = 2 * (sqrt(3) / 4) * x^2
Given that there are two lateral faces, the total white cardboard needed is:
2 * (sqrt(3) / 4) * x^2 = sqrt(3) * x^2 / 2
We need to know the side length x of the equilateral triangle base in order to calculate the exact amount of white cardboard needed. Once we have the side length, we can substitute it into the formula to find the answer.
The surface area of an equilateral triangle can be calculated using the formula:
Area = (sqrt(3) / 4) * side length^2
Since each lateral face of the triangular prism is an equilateral triangle, we need to find the side length x of the equilateral triangle base. The height h of the triangle can be calculated as h = x * sqrt(3) / 2.
Now, the lateral surface area of the pizza container can be calculated as:
lateral surface area = 2 * lateral face area = 2 * (sqrt(3) / 4) * x^2
Given that there are two lateral faces, the total white cardboard needed is:
2 * (sqrt(3) / 4) * x^2 = sqrt(3) * x^2 / 2
We need to know the side length x of the equilateral triangle base in order to calculate the exact amount of white cardboard needed. Once we have the side length, we can substitute it into the formula to find the answer.
1 answer