Answer :
The scale factor of area of the drawing to the area of the office is the
square of the scale factor of the length of the drawing.
- The area of the office space is 192 square yards.
Reasons:
The given parameters are;
1 inch in the scale drawing = 4 yd. in actual dimension
4 yd. = 144 inches
Therefore;
1 inch in the scale drawing = 144 inches in actual dimension
The scale factor of length of the drawing, s = 1:144
The scale factor of area = s²
Therefore, we have;
- [tex]\dfrac{Drawing \ area}{Actual \ area} =s^2[/tex]
Therefore, we have;
- [tex]\dfrac{Drawing \ area}{Actual \ area} =\dfrac{12}{A} = s^2 = \left( \dfrac{1}{144} \right)^2[/tex]
Where;
A = The actual office space area
There fore;
12 × 144² = A × 1²
A = 12 × 144² = 248,832 in.²
1 yd.² = 1,296 in.²
- [tex]248,832 \, in.^2 = \dfrac{248,832}{1,296} \, yd.^2 = 192 \, yd.^2[/tex]
The area of the office space is 192 square yards.
Lear more here:
https://brainly.com/question/17166840