Pedro uses cardboard to make a model of a square pyramid. The edges of the base of the model are 5 In.long. the height of each triangular face is 4 in. What is the area of the cardboard in Pedro's model? Show your work.
To find the area of the cardboard in Pedro's model, we need to calculate the area of each face of the square pyramid.
The base of the square pyramid is a square with edges measuring 5 inches each. Therefore, the area of the base is calculated by multiplying the length of one side by itself, which is 5 * 5 = 25 square inches.
The square pyramid has 4 triangular faces. Each triangular face has a base length of 5 inches (equal to the edge length of the square base) and a height of 4 inches.
The formula to calculate the area of a triangle is 1/2 * base * height. Therefore, for each triangular face, the area is calculated as 1/2 * 5 * 4 = 10 square inches.
Since there are 4 triangular faces, the total area of the triangular faces is 4 * 10 = 40 square inches.
The total area of the cardboard in Pedro's model, including the base and the 4 triangular faces, is given by the sum of the areas of the base and the triangular faces, which is 25 + 40 = 65 square inches.
Therefore, the area of the cardboard in Pedro's model is 65 square inches.
To find the area of the cardboard in Pedro's model, we need to find the area of each face of the square pyramid and then sum them up.
The area of each triangular face is 1/2 * base * height.
For Pedro's model, the base of each triangular face is one edge of the square base, which is 5 inches long. The height of each triangular face is given as 4 inches.
So, the area of each triangular face is 1/2 * 5 in * 4 in = 10 square inches.
Since there are 4 triangular faces in a square pyramid, we can multiply the area of one triangular face by 4 to find the total area of the triangular faces.
Total area of the triangular faces = 10 sq in * 4 = 40 square inches.
Next, we need to find the area of the square base of the pyramid. The base is a square, so its area is just the length of one side squared. In this case, the length of one side of the square base is given as 5 inches.
Area of the square base = 5 in * 5 in = 25 square inches.
To find the total area of the cardboard in Pedro's model, we add the area of the triangular faces and the area of the square base.
Total area of the cardboard = Area of triangular faces + Area of square base
= 40 square inches + 25 square inches
= 65 square inches.
Therefore, the area of the cardboard in Pedro's model is 65 square inches.
To find the area of the cardboard in Pedro's square pyramid model, we need to calculate the surface area of all the individual faces of the pyramid.
1. Start by finding the area of the base of the pyramid. Since the base is a square, the area is calculated by multiplying the length of one side by itself. In this case, each side of the base is 5 inches long, so the area of the base is 5 inches * 5 inches = 25 square inches.
2. Next, find the area of each triangular face. The formula to calculate the area of a triangle is (base * height) / 2. In this case, the base of each triangle is the same as the side length of the base of the pyramid, which is 5 inches. The height of each triangular face is given as 4 inches. Therefore, the area of each triangular face is (5 inches * 4 inches) / 2 = 20 square inches.
3. Since the pyramid has four identical triangular faces, multiply the area of one triangular face by four to account for all four faces. Thus, the total area of the four triangular faces is 20 square inches * 4 = 80 square inches.
4. Finally, calculate the total area of the cardboard in Pedro's model by adding the area of the base (25 square inches) to the area of the four triangular faces (80 square inches). 25 square inches + 80 square inches = 105 square inches.
Therefore, the area of the cardboard in Pedro's model is 105 square inches.