Black building

Jozef built a building with a rectangular footprint of 3.9 m × 6.7 m. Calculate by what percentage the building exceeds the legal limit of 25 m² for a small building. A building constructed without planning permission is called an illegal building. Also calculate the angle between the walls that would keep the footprint within the 25 m² limit, given the same wall lengths, if the building were built with a non-rectangular shape.

Final Answer:

p =  4.5 %
α =  73.0884 °

Step-by-step explanation:

$$\begin{gathered} a=3.9\text{m} \\ b=6.7\text{m} \\ {S}_1=25{\text{m}}^2 \\ {S}_2=a\cdot b=3.9\cdot 6.7=\frac{2613}{100}=26.13{\text{m}}^2 \\ p=100\cdot \frac{S_2-S_1}{S_1}=100\cdot \frac{26.13-25}{25}=4.5\% \end{gathered}$$

$$\begin{gathered} S_1=S_2\cdot \sin \alpha \\ A=\arcsin (S_1/S_2)=\arcsin (25/26.13)\doteq 1.2756\text{rad} \\ \alpha =A\to \text{°}=A\cdot \frac{180}{\pi }\text{°}=1.2756\cdot \frac{180}{\pi }\text{°}=73.088\text{°}=73.0884^{\circ }=73°5^{\prime }18" \end{gathered}$$

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