Question

1. what is the actual area of the front wall of the house? scale: 1 cm = 3 m

Explanation:

Step1: Convert side - length to actual length

Since the scale is $1\ cm = 3\ m$, for a side - length of $3\ cm$ on the drawing, the actual side - length $a$ is $a=3\times3 = 9\ m$.

Step2: Calculate the area of the triangle

The area formula for an equilateral triangle is $A=\frac{\sqrt{3}}{4}a^{2}$. Substituting $a = 9\ m$ into the formula, we get $A=\frac{\sqrt{3}}{4}\times9^{2}=\frac{81\sqrt{3}}{4}\approx35.07\ m^{2}$.

Answer:

$\frac{81\sqrt{3}}{4}\ m^{2}\approx35.07\ m^{2}$