Kevin Raps, a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift box 4.33 inches and 5 inches if all the triangles are equilateral how much wrapping paper did he use in square inches?
To find the total amount of wrapping paper used, we need to calculate the area of each triangular face of the pyramid and then add them all together.
Each face of the triangular pyramid is an equilateral triangle, which means all sides are equal. The formula to calculate the area of an equilateral triangle is A = (s^2 * sqrt(3)) / 4, where s is the length of the side.
Given that the side length of the triangle is 4.33 inches, we can calculate the area of one triangular face:
A = (4.33^2 * sqrt(3)) / 4
A ≈ 7.5 square inches
Since there are 3 identical faces on the triangular pyramid, we multiply the area of one face by 3 to get the total amount of wrapping paper used for the triangular faces:
Total triangular faces wrapping paper = 7.5 * 3 = 22.5 square inches
Next, we need to calculate the area of the square base of the pyramid:
Area of the square base = 5 * 5 = 25 square inches
Finally, we add the areas of the triangular faces and the square base to get the total wrapping paper used:
Total wrapping paper = 22.5 + 25 = 47.5 square inches
Therefore, Kevin used 47.5 square inches of wrapping paper for his triangular pyramid gift box.