1. What is the surface area of the pyramid shown to the nearest whole number? The diagram is not drawn to scale.
The lengths are, 3ft as the base, 3ft as the width, and the height is going up at an angle on the outside face on the pyramid which is 8ft.
A) 21ft^2
B) 48ft^2
C) 57ft^2
D) 105ft^2
Is the answer C?
it’s C)57 ft^2
the answer is 57 ft2
To determine the surface area of a pyramid, we need to add up the areas of all its faces. In this case, we have a pyramid with a rectangular base and four triangular faces.
First, let's calculate the area of the base. The base is a rectangle with a length of 3 ft and a width of 3 ft, so its area is 3 ft * 3 ft = 9 ft^2.
Now, let's calculate the area of each triangular face. Since the diagram is not to scale, we need to use the given dimensions to find the height of each triangular face. The height of the pyramid is given as 8 ft, but we need the height of the triangular face, which will be different due to the slant.
To find the height of each triangular face, we can use the Pythagorean theorem. The hypotenuse of each triangular face is the slant height of the pyramid, which is 8 ft. The base of each triangular face is the width of the base rectangle, which is 3 ft. Let's call the height of each triangular face "h."
Using the Pythagorean theorem, we can calculate the height of each triangular face:
h^2 + 3^2 = 8^2
h^2 + 9 = 64
h^2 = 64 - 9
h^2 = 55
h = √(55) ≈ 7.42 ft
Now that we have the height of each triangular face, we can calculate their areas. The area of a triangle is given by the formula A = 1/2 * base * height.
The area of each triangular face is 1/2 * 3 ft * 7.42 ft = 11.13 ft^2. Since there are four triangular faces, the total area of the triangular faces is 4 * 11.13 ft^2 = 44.52 ft^2.
Finally, to get the surface area of the pyramid, we add the area of the base and the area of the triangular faces: 9 ft^2 + 44.52 ft^2 ≈ 53.52 ft^2.
Now, let's compare that to the given answer choices:
A) 21 ft^2
B) 48 ft^2
C) 57 ft^2
D) 105 ft^2
The closest answer to the calculated surface area, 53.52 ft^2, is C) 57 ft^2. Therefore, the answer is C).
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how did you get that?
Are we including the area of the base ?
Yes I did. I used =lw+l then square(w
2)2+h2
+w square(l
2)2+h2