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, we first need to find the slant height of the pyramid using the Pythagorean Theorem:
s² = (7²/4) + (s/2)²
s² = 49/4 + s²/4
s²/4 = 49/4
s/2 = 7/2
s = 7√2/2
Now we can substitute this value into the formula for the surface area:
SA = s² + 2(1/2)(s)(s/2)
SA = s² + s²
SA = 2s²
If the base edge length is 2.5 in, then:
s = 2.5√2/2 = 1.768 in
Substituting this value into the formula:
SA = 2(1.768)² = 6.244 in² (rounded to three decimal places)
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