We know that the original painting of Mona Lisa is 77 centimeters by 53 centimeters. The enlarged version on a billboard is similar to it, with a linear scale factor of 20. We want to find the area of the billboard. Let's first find the area of the original painting.
Original Painting
The area of a rectangle with length l and width w equals l w. In our case, we can treat 77 centimeters as the length, and 53 centimeters as the width. Let's substitute 77 for l and 53 for w in the formula for area A.
A = 77( 53) = 4081The original painting has an area of 4081 square centimeters.
Billboard's Area
Now, let's find the billboards area. Let's first recall that the area scale factor between similar figures is a square of their linear scale factor.
Area scale factor
=
( Linear scale factor )^2
In our case, the linear scale factor is 20, so the area scale factor is 20^2 = 400. To get the billboard's area we should multiply the painting's area by 400. Let's do it!
4081 * 400 = 1 632 400
The billboard's area is 1 632 400 square centimeters.
