Question

you are planning to use a ceramic tile design in your new bathroom. the tiles are blue-and-white equilateral triangles. you decide to arrange the blue tiles in a hexagonal shape as shown. if the side of each tile measures 4 centimeters, what will be the approximate area of each hexagonal shape? 4 cm options: 12 cm², 192 cm², 41.6 cm², 55.4 cm²

Explanation:

Step1: Identify hexagon composition

The hexagon is 6 equilateral triangles, each with side 4 cm.

Step2: Area of one equilateral triangle

Formula: $\frac{\sqrt{3}}{4}s^2$. Substitute $s=4$: $\frac{\sqrt{3}}{4}×4^2 = 4\sqrt{3}$ cm².

Step3: Total area of hexagon

Multiply by 6: $6×4\sqrt{3} = 24\sqrt{3}$ cm².

Step4: Approximate value

$\sqrt{3}≈1.732$, so $24×1.732≈55.4$ cm².

Answer:

D. 55.4 cm²