Answer
34 in$^{2}$
Work Step by Step
A = $\sqrt {s(s-a)(s-b)(s-c)}$ where s = $\frac{1}{2}$(a+b+c)
a = 8
b = 9
c = 10
To simplify the equation and make the computation process easier, solve for "s" first.
s = $\frac{1}{2}$(a+b+c) = $\frac{1}{2}$(8+9+10) = $\frac{1}{2}$(27) = 13.5
Now, substitute 13.5 into the original equation every time "s" appears.
A = $\sqrt {s(s-a)(s-b)(s-c)}$
A = $\sqrt {13.5(13.5-a)(13.5-b)(13.5-c)}$
A = $\sqrt {13.5(13.5-8)(13.5-9)(13.5-10)}$
A = $\sqrt {13.5(5.5)(4.5)(3.5)}$
A = $\sqrt {1169.4375}$
A $\approx$ 34.2
34.2 rounded to the nearest whole number is 34.
