Insulate house

The property owner wants to insulate his house. The house has these dimensions of 12, and 12 m is 15 m high. The windows have six 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 =  700.45 m²

Step-by-step explanation:

$$\begin{gathered} a=12\text{m} \\ c=15\text{m} \\ n=6 \\ {o}_1=170\text{cm}\to \text{m}=170:100\text{m}=1.7\text{m} \\ {o}_2=150\text{cm}\to \text{m}=150:100\text{m}=1.5\text{m} \\ {v}_1=250\text{cm}\to \text{m}=250:100\text{m}=2.5\text{m} \\ {v}_2=170\text{cm}\to \text{m}=170:100\text{m}=1.7\text{m} \\ o=4\cdot a=4\cdot 12=48 \\ {S}_1=o\cdot c=48\cdot 15=720{\text{m}}^2 \\ {S}_2=n\cdot o_1\cdot o_2=6\cdot 1.7\cdot 1.5=\frac{153}{10}=15.3{\text{m}}^2 \\ {S}_3=v_1\cdot v_2=2.5\cdot 1.7=\frac{17}{4}=4.25{\text{m}}^2 \\ x=S_1-S_2-S_3=720-15.3-4.25=700.45{\text{m}}^2 \end{gathered}$$

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