The Washington Monument is 169 meters tall with a square base 16.8 m wide. An artist plans to construct a replica on the shore of Lake Michigan in Wisconsin, using a scale factor of 1:8.

What is the area of the replica’s base?

Respuesta :

Answer:

The area of the replica’s base would be 4.41 m².

Step-by-step explanation:

Given,

The base of the monument is a square of length 16.8 m.

That is, the actual side length of the base = 16.8 m

Scale factor = [tex]\frac{1}{8}[/tex]

Now,

[tex]\text{Scale factor}=\frac{\text{Scaled measure}}{\text{Actual measure}}[/tex]

[tex]\frac{1}{8}=\frac{\text{Scaled measure}}{16.8}[/tex]

[tex]\implies \text{Scaled measure} = \frac{16.8}{8}=2.1[/tex]

Thus, the side length of the replica's base is 2.1 m.

The base of replica is also a square.

Area of the base of replica = side²

                                             = 2.1²

                                             = 4.41 m²

Therefore, the area of the replica’s base would be 4.41 m².