What is the surface area of the square pyramid if the altitude is 4 cm, the length is 6 cm, and the height is 5 cm?
a. 48 cm^2
b. 144 cm^2
c. 156 cm^2
d. 96 cm^2
i think the answer is 144 cm^2. Please show me how you did the work so then i know that i at least got partial credit.
If the height of each triangular face is 4, then the area including base is
36 + 4*6*4/2 = 84
without the base, it's 48
If it is 5, then the area is
36 + 4*6*5/2 = 96
without the base, it's 60
So, you can see that much important information has been omitted. The answer is: If you want useful responses, you must provide useful data.
To find the surface area of a square pyramid, you need to calculate the sum of the areas of all the individual faces.
A square pyramid has five faces: the base, which is a square, and four triangular faces. Let's calculate each face separately:
1. Base: The base of the pyramid is a square, so its area is the length of one side squared. Given that the length of a side is 6 cm, the area of the base is 6 cm × 6 cm = 36 cm^2.
2. Triangular faces: Each triangular face has a base equal to the length of a side of the square base and a height the same as the given altitude. The area of a triangle is calculated using the formula 1/2 × base × height.
Since the length of a side of the base is 6 cm, and the altitude is 4 cm, the area of each triangular face is 1/2 × 6 cm × 4 cm = 12 cm^2.
Since there are four triangular faces, the total area of all the triangular faces is 12 cm^2 × 4 = 48 cm^2.
Finally, to find the total surface area, you add the area of the base and the area of the four triangular faces: 36 cm^2 + 48 cm^2 = 84 cm^2.
Therefore, the correct answer is not among the given options.
what is the difference between altitude and height?
144 = 36 + 4*27
I can't "square" that with the dimensions given, assuming the base is 6x6.
So, what's the difference between the height and the altitude?