In the shape above each yellow square has an area of 1 square unit. What is the area of the blue star?
+128408 Notice that the diagonal of each of the yellow squares = sqrt (1^2 + 1^2) = sqrt (2)
So....the width of the yellow square at the top = sqrt (2)
And if we draw a segment connecting the bottom edges of the two squares directly adjacent to this top square we will form two (blue) right triangles each with a base of sqrt (2) / 2 and a height of 1
So the area of each of these triangles = (1/2)( sqrt (2)/2) (1) = sqrt (2)/4
And we have 8 such triangles ....so their total area = 8 * sqrt (2) / 4 = 2sqrt (2)
And the remaining part of the star is just a square with a side length of sqrt (2)
So this area = (sqrt (2))^2 = 2
So....the total area of the blue star = 2sqrt (2) + 2 = 2 (sqrt (2) + 1) ≈ 4.828 units^2
