Insulate house

The property owner wants to insulate his house. The house has these dimensions 12, and 12 m is 15 m high. The windows have 6 with dimensions 170 and 150 cm. Entrance doors are 250 and 170 cm in size. How many square meters of polystyrene does he need?

Correct answer:

x =  689.4 m²

Step-by-step explanation:

$$\begin{gathered} a=12\text{ m } \\ c=15\text{ m } \\ n=6 \\ {o}_1=170\text{ cm}\to \text{ m}=170\mathrm{/}100\text{ m}=1.7\text{ m } \\ {o}_2=150\text{ cm}\to \text{ m}=150\mathrm{/}100\text{ m}=1.5\text{ m } \\ {v}_1=250\text{ cm}\to \text{ m}=250\mathrm{/}100\text{ m}=2.5\text{ m } \\ {v}_2=170\text{ cm}\to \text{ m}=170\mathrm{/}100\text{ m}=1.7\text{ m } \\ o=4\cdot a=4\cdot 12=48 \\ {S}_1=o\cdot c=48\cdot 15=720{\text{m}}^2 \\ {S}_2=n\cdot o_1\cdot o_2=6\cdot 1.7\cdot 1.5={\displaystyle \frac{153}{10}}=15.3{\text{m}}^2 \\ {S}_3=v_1\cdot v_2=2.5\cdot 1.7={\displaystyle \frac{17}{4}}=4.25{\text{m}}^2 \\ x=S_1-S_2-S_2=720-15.3-15.3=689.4{\text{m}}^2 \end{gathered}$$

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