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.403.1 in.
B.503.1 in.
C.1,119.6 in.
D.1,379.4 in.

Answer 1

Area of the squares (6):
A 1 = 6 · 10² = 600 in²
Area of the equilateral triangles (6):
A 2 = 6 · 10²√3 / 4 = = 6 · 25 · 1.73 = 259.8 in²
Area of the hexagon:
A 3 = 6 · 10²√3/4 = 259.8 in²
Total area:
600 + 259.8 + 259.8 = 1,119.6 in²
Answer: C )