Five congruent squares each of area 14 support a larger square. What area is shaded?
Scroll down for a solution to this problem.
Solution
The shaded area is 5.
The solution goes as follows:
- Calling the small square side a, we can use the Pythagorean theorem to find that the large square has side a√5.
- Drawing the line segment from vertex E to the midpoint P, it is easily seen from the two equal angles that it is parallel to the segment JL. Its length can, again using Pythagoras, be found to be 5a/2.
- From similarity of triangles EPO and LJO, the proportion of EO : OL is seen to be 5 : 2.
- Using the fact that triangles with equal height have area proportions equal to their base proportions, we fill in areas 2A, 5A and 14A.
- Finally, we use a=√14 in the large triangle to find that A=1.
Poem
A container on a ship can contain
A lot of things, treasures, weapons, furnitures
It’s a metaphor, a container
can be
Our spirit with thoughts, dreams, poems
A part of our humanity
Sailing on the waves of our lifes
With our stories, our wishes, our bodies