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) = 4081
The 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.
