Write and simplify an expression for the surface area of a square pyramid with a base edge length of s in. and triangular faces with a height of 7 in. What is the surface area if the base edge length is 2.5 in.?
SA = s2 + ? s
The surface area is ? in2.
To simplify the expression for the surface area, we need to find the slant height of the pyramid. This can be found using the Pythagorean theorem:
slant height = √(s/2)^2 + 7^2
slant height = √(s^2/4 + 49)
Now we can use the formula for the surface area of a square pyramid:
SA = s^2 + 2s * slant height
Plugging in the expression for the slant height:
SA = s^2 + 2s * √(s^2/4 + 49)
To find the surface area when s = 2.5 in., we simply plug in that value:
SA = (2.5)^2 + 2(2.5) * √((2.5)^2/4 + 49)
SA = 10.625 + 2(2.5) * √(6.5625 + 49)
SA = 10.625 + 5√55
SA ≈ 23.975 in^2 (rounded to three decimal places)
So the
SA = s2 + ? s = ? = 23.975?
The surface area is 23.975 in2.
No, the expression SA = s2 + ? s is not the simplified expression. The simplified expression is:
SA = s^2 + 2s * √(s^2/4 + 49)
And when s = 2.5 in., the surface area is approximately 23.975 in^2. So the correct answer is:
SA = 23.975 in^2
Wait but you HAVE to simplify that expresion..... (please!!)
SA = s2 + s
The surface area is in2.
I'm sorry, but the expression SA = s2 + s is not the correct simplified expression for the surface area of a square pyramid with a base edge length of s in. and triangular faces with a height of 7 in.
The correct simplified expression is:
SA = s^2 + 2s * √(s^2/4 + 49)
This expression cannot be simplified any further because it involves square roots and cannot be expressed as a simple polynomial.
When the base edge length is 2.5 in., plugging in the value of s into this expression, we get:
SA = (2.5)^2 + 2(2.5) * √((2.5)^2/4 + 49)
SA ≈ 23.975 in^2
Okay........ So what's the Surface Area><?
When the base edge length is 2.5 in, the surface area of the square pyramid is approximately 23.975 in².
It was wrong...
I apologize for the error in my previous response. When the base edge length is 2.5 in, the surface area of the square pyramid is:
SA = s^2 + 2s * √(s^2/4 + 49)
SA = (2.5)^2 + 2(2.5) * √((2.5)^2/4 + 49)
SA = 6.25 + 2(2.5) * √(0.625 + 49)
SA = 6.25 + 5√50
SA ≈ 29.8 in²
So the surface area of the pyramid is approximately 29.8 in² when the base edge length is 2.5 in.