Cavalieri Areas

Geometry Level 1

In the figure below, the three blue arrows are of equal length.

Which area is larger?

Clarification:

  • The top and bottom line of all the shapes touch the grey rectangle.
  • If a line parallel to the base of the rectangle is drawn anywhere, it cuts all the shapes at equal lengths.
All areas are equal Green Red Yellow

Agnishom Chattopadhyay by Agnishom Chattopadhyay , 22, India

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2 solutions

Alex Wang
Nov 28, 2017

cut the shapes and move the pieces so it becomes rectangle

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ayush Kumar
Aug 17, 2017

The rectangle and parallelogram are of equal area given that they have the same base and height. The arc is actually simple. Just as the parallelogram, we can take the outward arc and move it to the hole in the area. Then, it becomes a simple rectangle congruent to the first and has the same area as the other two.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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