Storage shed

Frank designed a net for a storage shed that he is going to construct out of metal. The design consists of a square base and four square sides, plus four triangular parts that make up the roof.

A square base of 6 feet and four square sides, plus 4 feet of four triangular parts that make a roof.

He has 250 square feet of metal to use to build the shed.

What is the surface area of the storage shed that Frank designed?
square feet

Does Frank have enough metal to construct his design?

Result

S =  228 ft²
x=

Yes

No

S =

Step-by-step explanation:

$$\begin{gathered} a=6\text{ft} \\ h=4\text{ft} \\ {S}_1=a^2=6^2=36 \\ {S}_2=\frac{a\cdot h}{2}=\frac{6\cdot 4}{2}=12{\text{ft}}^2 \\ S=5\cdot S_1+4\cdot S_2=5\cdot 36+4\cdot 12=228{\text{ft}}^2 \end{gathered}$$

$$\begin{gathered} S<250{\text{ft}}^2 \\ x=1 \end{gathered}$$

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