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I REALLY NEED HELP FOR THIS ONE

I REALLY NEED HELP FOR THIS ONE-example-1
User Bludzee
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1 Answer

7 votes

Answer:

A = 27(2√3-π) cm² ≈ 8.71 cm²

Explanation:

Area of shaded region it is area of hexagon minus area of circle.

A regular hexagon is comprised of six equilateral triangles (of the same sides).

So its area:
A_1=6\cdot(S^2\sqrt3)/(4)=\frac{3S^2\sqrt3}2 {S = side of the triangle}

Height (H) of such a triangle is equal to radius (R) of a circle inscribed in the hexagon:


R = H = (S\sqrt3)/(2)

Area of shaded region:


A=A_1-A_\circ=\frac{3S^2\sqrt3}2-\pi R^2=\frac{6S^2\sqrt3}4-\pi\left(\frac{S\sqrt3}2\right)^2=\frac{S^2(6\sqrt3-3\pi)}4

S = 6 cm

so:


A=\frac{6^2(6\sqrt3-3\pi)}4=\frac{36(6\sqrt3-3\pi)}4=9(6\sqrt3-3\pi)=27(2\sqrt3-\pi)\ cm^2\\\\A=27(2\sqrt3-\pi)\ cm^2\approx8.71\ cm^2

I REALLY NEED HELP FOR THIS ONE-example-1
User Tarik Huber
by
8.6k points

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