How do you find the area of a regular hexagon with a radius of 5? Please show working.

Answer 1

#A = (75 sqrt(3))/2 ~~65 " units"^2#

Given: a regular hexagon with radius = 5

#A = 1/2 a P#, where #a# = apothem , #P# = perimeter

The apothem is the perpendicular distance from the center to a side.

#(cos 30^@)/1 = a/r = a/5; " " a = 5 cos 30^@ = (5 sqrt(3))/2 #

#A = 6ax = 6 ((5 sqrt(3))/2) (5/2) = (75 sqrt(3))/2 ~~64.95 " units"^2#

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Answer 2

To find the area of a regular hexagon with a radius of 5, you can follow these steps:

  1. Find the apothem (distance from the center to the midpoint of a side) of the hexagon using the formula: ( \text{apothem} = \frac{\sqrt{3}}{2} \times \text{side length} ).

    Given that the radius ( r = 5 ) and the hexagon is regular, the side length ( s ) can be calculated as ( s = 2r = 2 \times 5 = 10 ).

    Substitute the side length into the apothem formula: ( \text{apothem} = \frac{\sqrt{3}}{2} \times 10 = 5\sqrt{3} ).

  2. Calculate the area of the hexagon using the formula: ( \text{area} = \frac{3}{2} \times \text{apothem} \times \text{side length} ).

    Substitute the values into the formula: ( \text{area} = \frac{3}{2} \times 5\sqrt{3} \times 10 = 75\sqrt{3} ).

Therefore, the area of the regular hexagon with a radius of 5 is ( 75\sqrt{3} ) square units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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