Serena is making a model of one of the Egyptian pyramids. The square base has sides that are all 4.8 in. Each of the triangular faces has a base of 4.8 in and a height of 4.2 in. How much paper would it take to cover the entire pyramid?
First, let's find the area of each triangular face using the formula:
Area = 1/2 * base * height
Area = 1/2 * 4.8 in * 4.2 in = 10.08 in^2
There are 4 triangular faces, so the total area of all the triangular faces is:
4 * 10.08 in^2 = 40.32 in^2
Now, let's find the area of the square base:
Area = side^2
Area = 4.8 in * 4.8 in = 23.04 in^2
Finally, we need to add up the areas of all the faces to get the total surface area of the pyramid:
Total Surface Area = Area of Base + Area of all Triangular Faces
Total Surface Area = 23.04 in^2 + 40.32 in^2
Total Surface Area = 63.36 in^2
Therefore, it would take 63.36 square inches of paper to cover the entire pyramid.
To calculate the amount of paper needed to cover the entire pyramid, we first need to find the area of each triangular face and the area of the square base.
The area of a triangle can be calculated using the formula:
Area = (base * height) / 2
For each triangular face:
Area = (4.8 in * 4.2 in) / 2 = 10.08 square inches
Since there are 4 triangular faces on the pyramid, the total area of all the triangular faces is:
10.08 square inches * 4 = 40.32 square inches
The area of the square base can be calculated by squaring the length of one side:
Area = (4.8 in)^2 = 23.04 square inches
To find the total surface area of the pyramid, we add the areas of the triangular faces and the square base:
Total Surface Area = 40.32 square inches + 23.04 square inches = 63.36 square inches
Therefore, it would take 63.36 square inches of paper to cover the entire pyramid.