A scale drawing of a square has a side length of 6 millimeters. The drawing has a scale of 1 mm : 7 km. Find the actual perimeter and area of the square.

A=1764km^2
P=168km

An actual square will ALWAYS have the same lengths on each of the 4 sides. Therefore it will be 6mm all around the square. There are different ways to solve this type of problem but we’ll go with this one.

First you want to understand that the scale is a ratio or a fraction. With fractions you multiply the numerator or denominator, but if you multiply or divide with one, you must with the other. In this case the ratio (we can put it in fraction form) is 1/7. Now you want to make it to where the 1 (because it is a mm) becomes 6 because that’s how many mm we have on each side. To do that you need to find what times 1 is equal to 6 (which is 6 itself).

Now that you found what the numerator will be, we need to also multiply 7 by 6 because what you do with one side you must do to the other. So 7*6 will be 42. Your new fraction (or ratio) is 6/42.

Finally you should know that since a square has 4 sides you need to multiply what one side length of the square is by 4 for the perimeter. Because 6mm is 42km (because of the ratio) then do 42*4 which is 168.

Finding the area is much simpler with the already known lengths, area is l*w, which in this case for the square is just two side lengths times eachother. 42*42= 1764.