A square within a square...

Geometry Level 3

Let ABCD be a square. An equilateral triangle is placed on each side of the square, such that the base covers the whole side. Now join up the e x p o s e d {exposed} corners of the equilateral triangles (only join a d j a c e n t {adjacent} corners) such that a larger square, PQRS, is formed. What is the value of a r e a o f P Q R S a r e a o f A B C D \frac{area of PQRS}{area of ABCD} ? ( give your answer to 2dp)


The answer is 3.73.

Curtis Clement by Curtis Clement , 23, United Kingdom

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.

1 solution

Mark Yates
May 11, 2015

Outer triangle PQA's area can be found with Area=1/2 PA AQ sin(A). Area PQRS is made up of 4 such triangles + 4 equilateral triangles+the original squares: 4(1/2s^2sin150)+4(s^2 sqsrt/4)+s^2 Divide the above equation by the original square = s^2 to get 2sin150+sqrt3+1=3.732

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...