Puzzles & Quizzes

Can You Find the Total Area of the Red Regions?

This brain teaser was originally given to 6th-grade math students in China, according to MindYourDecision's Preshtal Walkar, a mathematics and economics graduate from Stanford.

Here's the Problem

You have a rectangle that measures 20 units long and 10 units tall. The rectangle has one of its diagonals connected. Inside the rectangle, there are two circles of equal size that are tangent to each other and to the rectangle. The area below the diagonal line inside the rectangle is filled in red, but the insides of the circles that are below the diagonal line are not filled it at all. What is the area of the red spots?

Watch the video below for the answer, as well as a more difficult version of this brain teaser. Or, scroll down to find the answer in text.

Can You Solve for the Area of the Red Regions?

This problem was supposedly given to 6th grade students in China.


The area of the red regions is 100 - 25π, which equals roughly 21.460. Watch the video above to find out how to arrive at this answer.

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Written by Curiosity Staff August 19, 2016

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