A winter valley

A rectangle and two triangles. What’s the total area?

Scroll down for a solution to this problem.


The total area is 30.

First, because all angles are the same, it is seen that the two triangles are similar. They have area proportion 9/4, so all lengths have proportion 3/2.

Now calling the base of the small triangle x, its height must be 8/x. Using the above proportionality, base and height of the large triangle can be found.

Finally, the rectangle area has area 3x/2*(8/x+12/x)=30.

Visual solution

A purely visual solution by David Andriana.


In a frozen valley
Kids are playing
The snow is falling
Cold is still feeling
No sun
No wind
The air is quiet
A bird, mighty, is flying
The snowy owl
Quebec’s symbol
The winter queen
With it’s majestic wings
She is flying quietly,
Hovering peacefully


🤞 Don’t miss these puzzles!

Subscribe to the weekly geometry puzzle e-mail.

Leave a Reply

Your email address will not be published. Required fields are marked *

Optionally add an image (JPEG only)