Question

The actual representation of a structure is given below.


If the length of the base in a scale drawing is 2 inch, find the area of the scale drawing of the structure.

• A. $\frac{25}{4}\text{sq. inch}$
• B. $\frac{50}{4}\text{sq. inch}$
• C. $\frac{25}{8}\text{sq. inch}$
• D. $\frac{50}{8}\text{sq. inch}$

Answer 1

The correct option is C $\frac{25}{8}\text{sq. inch}$

Actual base length of the structure = 8 ft
Base length of the scale drawing = 2 in

$\text{So, the scale is =}2in:4ft$
$=1in:4ft$

We know, 1 feet = 12 inch.
$\therefore 4feet=4\times 12=48inch$

$\text{So, Scale factor =}\frac{1}{48}$

Now, Area of actual struture is =
Area of triangle + Area of the two rectangles
$=(\frac{1}{2}\times 2\times 2)+(5\times 8)+(8\times 1)$
$=50sq.ft$

$\text{Area of the scale drawing =}$
$\text{Actual area}\times (\text{Scale factor}{)}^2$
$=50\times (\frac{1}{48}{)}^2$

$=50\times \frac{1}{48}\times \frac{1}{48}sq.ft$

$=\frac{50\times 12\times 12}{48\times 48}sq.inch$

$=\frac{50}{16}sq.inch$

$=\frac{25}{8}sq.inch$

$\text{Area of scale drawing =}\frac{25}{8}\text{sq.inch}$