To find the surface area of the pyramid, we need to find the area of the base (the square) and the total area of the 4 triangular faces.
First, let's find the area of the base (the square):
The length of one side of the square is 4 feet, so the area of the base is 4 * 4 = <<4*4=16>>16 square feet.
Next, we need to find the area of one of the triangular faces, and then multiply it by 4 to get the total area of all the triangular faces.
The height of each triangular face can be found using the Pythagorean theorem. In this case, since we have a right triangle with hypotenuse (the dashed line) of 7 feet, and one leg (half of the square's side) of 2 feet, the height can be found by solving for the other leg in the equation:
h^2 + 2^2 = 7^2
h^2 + 4 = 49
h^2 = 45
h = sqrt(45) = 3 * sqrt(5)
Now we can find the area of one triangle:
The base of the triangle is 4 feet and the height is 3 * sqrt(5), so the area is:
Triangle_area = 0.5 * base * height
Triangle_area = 0.5 * 4 * (3 * sqrt(5))
Triangle_area = 6 * sqrt(5)
Since there are 4 triangles, the total area of the triangles is 4 * (6 * sqrt(5)) = 24 * sqrt(5) square feet.
Now, let's add the area of the base to the area of the triangles to find the surface area of the pyramid:
Surface_area = Base_area + Triangles_area
Surface_area = 16 + 24 * sqrt(5) ≈ 53.67 square feet.
So the surface area of the regular pyramid is approximately 53.67 square feet.
find the surface area of the regular pryamid
A pyramid with a square base is shown. The sides of the square base measure 4 feet. A dashed line which is labeled 7 feet extends from the middle of a side of the base along a triangular surface to the vertex at the top of the pyramid.
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