How do you find the area of a regular hexagon with a radius of 5? Please show working.
Given: a regular hexagon with radius = 5
The apothem is the perpendicular distance from the center to a side.
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To find the area of a regular hexagon with a radius of 5, you can follow these steps:

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} ).

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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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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