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Need help with these two math questions. Can someone please help me?

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2 Answers

sin 45o = 1/√2, also known as ½√2 (rationalized denominator).
 
To figure the area of a regular hexagon, draw one of the central angles (it measures 60o) and note the triangle formed by the two radii and one of the sides of the hexagon--all 3 sides of this triangle are= r, radius of the circumscribing circle.
 
The equilateral triangle has area ¼r2√3...(standard formula for equilateral triangle of side r).  So just multiply that by six to account for the entirety of the regular hexagon.
sin 45º=√2/2  (look on the unit circle)
 
area of a regular polygon given the side length...
here's the formula without the derivation; if you need the derivation I will write it out...
A=(n)(s2)/4tanθ where n=# of sides, s=side length, and θ=(1/2)(360/n)=180/n
n=6, s=4 m, θ=45º
 
A=(6)(42)/4tan(45º)
A=(6)(16)/[(4)(1)]
A=(96)/4
A=24 square meters  (sin45º=√2/2 and cos45º=√2/2 and tan=sin/cos so tan45º=1)