Question

the scale from a square park to a drawing of the park is 5 m to 1 cm. the actual park has an area of 1,600 m². what is the area of the drawing of the park? show your work.

Explanation:

Step1: Find the side - length of the actual park

Since the area of a square is $A = s^2$ and $A = 1600$ m², then $s=\sqrt{1600}=40$ m.

Step2: Find the side - length of the park in the drawing

The scale is 5 m to 1 cm. So if the actual side - length $s = 40$ m, then the side - length in the drawing $s_d=\frac{40}{5}=8$ cm.

Step3: Calculate the area of the park in the drawing

The area of the square in the drawing $A_d=s_d^2$. Substituting $s_d = 8$ cm, we get $A_d=8^2 = 64$ cm².

Answer:

64 cm²