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A pyramid on its side is shown with its height measuring 22 m and its base measuring 8 m.
Find the lateral area of the square pyramid.
I know how to do all of this but I forgot how to find the perimeter of the base.
can you work it out
First, let's find the slant height of the pyramid using the Pythagorean theorem. The slant height (l) can be found by:
l^2 = h^2 + (s/2)^2
Where h is the height of the pyramid and s is the length of one side of the base.
Plugging in the given values, we have:
l^2 = 22^2 + (8/2)^2
l^2 = 484 + 16
l^2 = 500
Taking the square root of both sides, we find:
l = √500
Next, we'll find the lateral area of the pyramid. The lateral area of a pyramid can be calculated using the formula:
lateral area = (1/2) * perimeter of base * slant height
Since the base of the pyramid is a square, the perimeter of the base (p) can be found by:
p = 4s
Plugging in the given values, we have:
p = 4 * 8
p = 32
Now, we can calculate the lateral area:
lateral area = (1/2) * 32 * √500
Simplifying further, we have:
lateral area = 16 * √500
To calculate the exact value, we can simplify the square root:
lateral area ≈ 16 * 22.36
lateral area ≈ 357.76
Therefore, the lateral area of the square pyramid is approximately 357.76 square meters.
The base has an area. It cannot be just 8 cm.
So, I assume you meant that the base is a square with sides 8 cm each.
In any case, the area is the square base (8^2) plus the area of the four triangular faces, each with base 8 and lateral height √(22^2-4^2)