Question

A. Write a formula that Brielle could use to find the square inches of cake she will cover in icing. Explain your formula.B. How many total square inches of icing will she need?

Answer 1

Given:

`\begin{gathered} a=c=6.5in \\ b=4in \\ h=3in \end{gathered}`

To find:

The surface area includes the top area of the cake.

Step-by-step explanation:

a) The formula of the surface area of the triangular prism is,

`\begin{gathered} A=Lateral\text{ surface area of the triangular prism+Top area} \\ A=(a+b+c)h+\frac{b\sqrt{a^2-(b^2)/(4)}}{2} \end{gathered}`

b) The surface area of the triangular prism is,

On substitution in the given formula we get,

`\begin{gathered} A=(6.5+6.5+4)*3+\frac{4\sqrt{6.5^2-(4^2)/(4)}}{2} \\ =17*3+2*√(42.25-4) \\ =51+2*√(38.25) \\ =51+2*6.1846 \\ =51+12.3693 \\ =63.369 \\ \approx63.4\text{ square inches} \end{gathered}`

Final answer:

The total square inches of icing will she need is 63.4 square inches.