Question

Part of a tiling design is shown. The center is a regular hexagon. A square is on each side of the hexagon, and an equilateral triangle joins the squares. Complete the pattern around the hexagon and calculate the total area of the pattern.

A.
322.0 in.²

B.
578.0 in.²

C.
716.6 in.²

D.
882.9 in.²

Answer 1

The area of the regular hexagon is:
A1 = 2.60 * (8) ^ 2
A1 = 166.4 in ^ 2
The area of the square is:
A2 = (8) * (8)
A2 = 64 in ^ 2
The area of the triangle is:
A3 = root ((s-a) * (s-b) * (s-c) * (s))
Where,
s = (a + b + c) / 2
s = (8 + 8 + 8) / 2
s = 24/2
s = 12
A3 = root ((12-8) * (12-8) * (12-8) * (12))
A3 = 27.71
Then, the area of the pattern is:
A = A1 + 6 * A2 + 6 * A3
Substituting:
A = 166.4 + 6 * (64) + 6 * (27.71)
A = 716.6 in ^ 2
Answer:
C.
716.6 in.²