Eight identical circles, each of radius one unit are arranged in a blue rectangle as shown. What is the area of the blue rectangle?
+128475 The base is easy.....it's just 6 units
And if we join the center of the top circle with the centers of the two middle circles we will have an equilateral triangle with sides of 2r
And the height, h, of one of these triangles can be found as
tan 60° = h
√3 = h
So....by symmetry.....the height of this rectangle = 2 + 2√3
So....its area =
6 (2 + 2√3) =
12 + 12√3 =
12 ( 1 + √3) units^2 ≈ 32.78 units^2
