+0

# geometry problem help?

0
41
4

Four equilateral triangles are constructed on the sides of a square with side length 1, as shown below. The four outer vertices are then joined to form a large square. Find the area of the large square.

Jul 21, 2020

#1
+8335
0

Let L be the side length of square.

By Law of Cosines,

$$L = \sqrt{1^2 + 1^2 - 2(1)(2)\cos 150^\circ} = \sqrt{2 + 2\sqrt 3}$$

Area of large square = $$L^2 = 2 + 2\sqrt 3$$

Jul 22, 2020
#3
0

Hi, Max! What are you doing here? Can you, please, explain it?

Guest Jul 22, 2020
#2
0

Area = ( 1 + 3 )2 / 2

Jul 22, 2020