Given:
[tex]\begin{gathered} a=c=6.5in \\ b=4in \\ h=3in \end{gathered}[/tex]
To find:
The surface area includes the top area of the cake.
Explanation:
a) The formula of the surface area of the triangular prism is,
[tex]\begin{gathered} A=Lateral\text{ surface area of the triangular prism+Top area} \\ A=(a+b+c)h+\frac{b\sqrt{a^2-\frac{b^2}{4}}}{2} \end{gathered}[/tex]
b) The surface area of the triangular prism is,
On substitution in the given formula we get,
[tex]\begin{gathered} A=(6.5+6.5+4)\times3+\frac{4\sqrt{6.5^2-\frac{4^2}{4}}}{2} \\ =17\times3+2\times\sqrt{42.25-4} \\ =51+2\times\sqrt{38.25} \\ =51+2\times6.1846 \\ =51+12.3693 \\ =63.369 \\ \approx63.4\text{ square inches} \end{gathered}[/tex]
Final answer:
The total square inches of icing will she need is 63.4 square inches.
