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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.^2
B.
503.1 in.^2
C.
1,119.6 in.^2
D.
1,379.4 in.^2

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 class=

Respuesta :

budwilkins
Since the squares are 10×10, 6 of them = 100×6=600in^2
There are 6 equilateral triangles around the hexagon, and the hexagon itself is made of 6 of those equilateral triangles. So 12× triangle's area will complete the total area.
Height of the triangle will split it into 2 30-60-90 triangles. So the h will be 5SR3, since the height will bisect the base (10) into 2 5's. And a 30-60-90 will have sides of x, xSR3, and 2x. Since x=5, the h will be 5SR3 = 8.66.
So area of the triangle:
1/2×b×h = 1/2×10×8.66 = 43.3
Now 12×43.3 = 519.62
Now add that to the 600 from the squares:
519.62 + 600 = 1,199.62 in^2
The correct answer is (C.)

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