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Two things will solve this guy faster: 1) know that a regular hexagon can be divided into six equal equilateral triangles, 2) know the formula used to calculate the area of an equilateral triangle using the side as a variable.
area of an equil triangle is [(side^2)*(sq root 3)]/4. so 6*[(side^2)*(sq root 3)]/4 = 24*(sq root 3). Solve for side = 4, which also = radius of circle. pi r^2 = 16 pi.
Area of 6 EQ triangle = 24 sqrt 3 Area of 1 Eq Triangle = 4 sqrt 3 0.5 * (2 x)* sqrt (3) x = 4 sqrt 3 x = 2 Area of circle pi (2 x)^2 = 16 pi Assumed The length of equ triangle = 2x which equals the radii of the circle
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Two things will solve this guy faster: 1) know that a regular hexagon can be divided into six equal equilateral triangles, 2) know the formula used to calculate the area of an equilateral triangle using the side as a variable.
ReplyDeleteAnswer is D
ReplyDeleteI am getting 32Pi..
ReplyDeletearea of equilateral triangle = 4root3
=0.5 X x/2 X (root3)/2 X x
x=4root2
area of circle = pi x X x
= 32pi
what gives?
area of an equil triangle is [(side^2)*(sq root 3)]/4. so 6*[(side^2)*(sq root 3)]/4 = 24*(sq root 3). Solve for side = 4, which also = radius of circle. pi r^2 = 16 pi.
ReplyDeleteOA D
ReplyDeleteArea of 6 EQ triangle = 24 sqrt 3
ReplyDeleteArea of 1 Eq Triangle = 4 sqrt 3
0.5 * (2 x)* sqrt (3) x = 4 sqrt 3
x = 2
Area of circle pi (2 x)^2 = 16 pi
Assumed The length of equ triangle = 2x which equals the radii of the circle