The smaller square in the diagram has side length 1. Equilateral triangles are constructed on its four sides, as shown. What is the area of the larger square?

Thanks in advance!!!

MIRB14
Jan 18, 2018

#1**+3 **

The area of the square is, of course, 1 square unit

Each of equilateral triangles has a side of 1, so their total area is

4 (1/2) * 1^2 * sin (60) = 2*√3/2 = √3 square units

The other 4 triangles have two sides of 1 and an included angle between these sides of

[360 - 90 - 60 - 60 ] = 150°

So...their area is

4 (1/2) * 1^2 * sin (150) = 2 * (1/2) = 1 square unit

So...the area of the larger square is ( 1 + 1 + √3) = [ 2 + √3 ] units^2

CPhill
Jan 18, 2018