Question

a scale drawing for a plot of land is shown below.
in the drawing, 4 cm represents 5 m.
assuming the backyard is rectangular, find the area of the real backyard.

area of the real backyard:

Explanation:

Step1: Find the scale factor

Given \(4\) cm represents \(5\) m. So, \(1\) cm represents \(\frac{5}{4}\) m.

Step2: Calculate the real - length of the backyard

The length of the backyard in the drawing is \(8\) cm. So, the real - length \(l = 8\times\frac{5}{4}=10\) m.

Step3: Calculate the real - width of the backyard

The width of the backyard in the drawing is \(12\) cm. So, the real - width \(w = 12\times\frac{5}{4}=15\) m.

Step4: Calculate the area of the backyard

The area of a rectangle \(A=l\times w\). Substituting \(l = 10\) m and \(w = 15\) m, we get \(A=10\times15 = 150\) \(m^{2}\).

Answer:

\(150\)