How to Measure the Height of Your House without getting on the Roof

We used shadows and proportionality to determine the height of our house.

My son is growing a coconut tree and wanted to know if it would grow to be taller than the house. Fortunately house height is easy to determine. All that's needed is a little sun, some measuring tools, something small with a known height and a little math.

The children's picture book Beanstalk: The Measure of a Giant (A Math Adventure) is a living math book which perfectly explains the process for measuring the height of something very tall. Jack, the main character from the fairy tale, climbs the beanstalk and meets a giant boy who becomes his friend. As the two boys play together they learn about proportionality by setting basketball nets at heights proportional to the heights of the boys. Reading about the boys setting the net at the proper height and their other adventures is a fun way for kids to learn this measuring trick.

First, the shadow of an object with a known height is measured.

Next, the shadow of the object with the unknown height is measured.

Finally an equation is written where the unknown height is represented as x. In this equation, 1 ft was the height of the ruler, 7 inches was the height of the ruler's shadow and 180 inches was the height of the house's shadow. Solving this equation we determined the house height to be approximately 25 feet tall. Therefore, if my son's coconut tree thrives in the German climate, it has the potential to grow taller than the house.