Real Area

Free interactive math game: Real Area — From map dimensions. Part of the Scale & Map category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. A rectangle on a map has dimensions: 5 cm × 6 cm Scale: 1 : 500 Find the real area in m².
  2. A rectangle on a map has dimensions: 4 cm × 3 cm Scale: 1 : 200 Find the real area in m².
  3. A rectangle on a map has dimensions: 8 cm × 7 cm Scale: 1 : 500 Find the real area in m².
  4. A rectangle on a map has dimensions: 7 cm × 6 cm Scale: 1 : 200 Find the real area in m².

About this exercise

How area behaves when lengths are scaled.

How to solve it

Area scales by the square of the length factor, because both the width and the height change.

Worked example

At 1 to 200, one square centimeter stands for 200 x 200 = 40000 square centimeters, that is 4 square meters.

Common mistake

Using the plain scale factor for area. Doubling every length multiplies the area by four, not by two.