Answer:
1.[tex]\boxed{\text{400 ft}^{2}}[/tex]; 2. [tex]\boxed{\frac{1}{3716}}[/tex]
Step-by-step explanation:
Step 1. Calculate the area of the floor
If the area A₁ of a square floor on the scale drawing is 100 cm², the length of a side is 10 cm.
The side length l of the actual floor is
l = 10 cm × (2 ft/1 cm) = 20 ft
The area A₂ of the floor is
A = l² = (20 ft)² = [tex]\boxed{\text{400 ft}^{2}}\\[/tex]
Step 2. Calculate the area ratios
We must express both areas in the same units.
Let's express the area of the room in square centimetres.
l = 20 ft × (12 in/1 ft) = 240 in
l = 240 in × (2.54 cm/1 in) = 609.6 cm
A₂ = l² = (609.6 cm)² = 371 612 cm²
The area A₁ on the scale drawing is 100 cm².
The ratio of the areas is
[tex]\frac{A_{1}}{ A_{2}} = \frac{100}{371612} = \frac{1 }{3716}\\[/tex]
The ratio of the area in the drawing to the actual area is [tex]\boxed{\frac{1}{3716}}[/tex]
