Serena is making a model of one of the Egyptian pyramids. The square base has sides that are all 4.2 in. Each of the triangular faces has a base of 4.2 in and a height of 3.6 in. How much paper would it take to cover the entire pyramid?
First, let's find the area of each triangular face:
Area = 1/2 x base x height
Area = 1/2 x 4.2 in x 3.6 in
Area = 7.56 sq in
There are four triangular faces, so the total area of the triangular faces is:
Total area of triangular faces = 4 x 7.56 sq in
Total area of triangular faces = 30.24 sq in
Now, let's find the area of the square base:
Area of base = side x side
Area of base = 4.2 in x 4.2 in
Area of base = 17.64 sq in
To cover the entire pyramid, we need to find the total surface area by adding the area of the base to the area of the triangular faces:
Total surface area = area of base + total area of triangular faces
Total surface area = 17.64 sq in + 30.24 sq in
Total surface area = 47.88 sq in
Therefore, it would take approximately 47.88 sq in of paper to cover the entire pyramid.
To find out how much paper it would take to cover the entire pyramid, we need to calculate the surface area of all the triangular faces.
The surface area of a triangle is given by the formula: Area = 1/2 * base * height.
Since the base and height of each triangular face are given as 4.2 in and 3.6 in respectively, we can calculate the area of each face:
Area = 1/2 * 4.2 in * 3.6 in
Area = 7.56 in²
Since there are four triangular faces on a pyramid with a square base, we can multiply the area of one face by four to find the total area of all the triangular faces:
Total area of triangular faces = 4 * 7.56 in²
Total area of triangular faces = 30.24 in²
Now, let's calculate the area of the square base:
The area of a square is given by the formula: Area = side * side
Area of the square base = 4.2 in * 4.2 in
Area of the square base = 17.64 in²
Finally, we add the area of the triangular faces to the area of the square base to find the total surface area of the pyramid:
Total surface area of the pyramid = Area of the square base + Total area of triangular faces
Total surface area of the pyramid = 17.64 in² + 30.24 in²
Total surface area of the pyramid = 47.88 in²
Therefore, it would take approximately 47.88 square inches of paper to cover the entire pyramid.