Painting a hut

It is necessary to paint the exterior walls of hut whose layout is a rectangle of 6.16 m x 8.78 m wall height is 2.85 meters. Cottage has five rectangular windows; three have dimensions of 1.15 m x 1.32 m and two 0,45 m x 0.96 m. How many m² is necessary to paint?

Correct result:

S =  79.74 m²

Solution:

$$\begin{gathered} a=6.16\text{ m } \\ b=8.78\text{ m } \\ c=2.85\text{ m } \\ o=2\cdot a+2\cdot b=2\cdot 6.16+2\cdot 8.78={\displaystyle \frac{747}{25}}=29.88\text{ m } \\ {S}_1=o\cdot c=29.88\cdot 2.85=85.158{\text{m}}^2 \\ {S}_2=3\cdot 1.15\cdot 1.32=4.554{\text{m}}^2 \\ {S}_3=2\cdot 0.45\cdot 0.96=0.864{\text{m}}^2 \\ S=S_1-S_2-S_3=85.158-4.554-0.864={\displaystyle \frac{3987}{50}}={\displaystyle \frac{3987}{50}}{\text{m}}^2=79.74{\text{m}}^2 \end{gathered}$$

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