Inconvenient Areas

Geometry Level 2

Both diagrams show squares of congruent lengths. On the left, the rhombus is formed by two midpoints on the square and two intersection points of identical circles. The yellow area is shaded as shown above.

Which diagram has the greatest amount of shaded area?

The left diagram. Both diagrams have the same area. The right diagram.

Michael Huang by Michael Huang , 29, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

David Vreken
Feb 1, 2021

Since you can cut and rearrange the shaded area as follows, the two areas are equal :

1 Helpful 2 Interesting 8 Brilliant 0 Confused
Lu Ca
May 4, 2021

It's easy to see that ABC triangle is congruent to BDE triangle.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Vin Benzin
Jan 31, 2021

The area of the diamond(including the white area) in the diagram on the left is 1/4 of the area of the whole square. That's the same area as one of the boxes surrounding a circle. If you just consider the circle contained inside a square, you see that the area surrounding the circle corresponds to the white area within the diamond in the diagram on the left and therefore the yellow areas are equal.

1 Helpful 0 Interesting 1 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...