Question

a scale drawing for a restaurant is shown below.
in the drawing, 3 cm represents 5 m.
assuming the dining hall is rectangular, find the area of the real dining hall.
(the image shows a diagram with a rectangle labeled kitchen with length 18 cm and height 6 cm, and a rectangle below it labeled dining hall with height 9 cm and width 6 cm.)

Explanation:

Step1: Find the scale factor

The scale is 3 cm represents 5 m. So the scale factor for length is $\frac{5\ m}{3\ cm}$.

Step2: Find the real length of the dining hall

The drawing length of the dining hall is 6 cm. Real length $l = 6\ cm\times\frac{5\ m}{3\ cm}= 10\ m$.

Step3: Find the real width of the dining hall

The drawing width of the dining hall is 9 cm. Real width $w = 9\ cm\times\frac{5\ m}{3\ cm}= 15\ m$.

Step4: Calculate the area of the rectangular dining hall

Area of rectangle $A=l\times w$. Substituting $l = 10\ m$ and $w = 15\ m$, we get $A = 10\times15=150\ m^{2}$.

Answer:

The area of the real dining hall is $\boldsymbol{150}$ square meters.