A map of square piece of property is drawn at a scale of 1 : 500. If a side of the property on the map is 16 cm, what is the property's actual area?

Question

asked May 25, 2018 216k views

2 Answers

Spitzbueb · Answer 1 · 2018-05-31T11:25:05+0000

Answer:

$\text{Actual area of property}}=6400\text{ m}^2$

Explanation:

Let x represent the actual side of square property.

We have been given that a map of square piece of property is drawn at a scale of 1 : 500.

We will use proportions to solve for our given problem.

$\frac{\text{Actual length}}{\text{Map length}}=(500)/(1)$

$\frac{x}{16\text{ cm}}=(500)/(1)$

$\frac{x}{16\text{ cm}}*16\text{ cm}=500*16\text{ cm}}$

$x=8000\text{ cm}$

$x=80\text{ m}$

We know that area of a square is square of its side length.

$\text{Actual area of property}}=(80\text{ m})^2$

$\text{Actual area of property}}=6400\text{ m}^2$

Therefore, the actual area of property is 6400 square meters.