Plz help me I have been stuck on this for soo long plzz! Well mark brainliest ONLY if u are correct!

Regular hexagon ABCDEF is inscribed in circle X and has an apothem that is 6√3 inches long. Use the length of the apothem to cal

Phantasy [73]

Answer:

Part A

$The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}$

Plugging in the given values we get;

$The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12$

R = 12 inches

The radius of the circumscribing circle is 12 inches

Part B

The length of each side of the hexagon, 's', is;

$s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)$

Therefore;

$s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12$

s = 12 inches

The perimeter, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon is 72 inches

Step-by-step explanation:

The given parameters of the regular hexagon are;

The length of the apothem of the regular hexagon, a = 6·√3 inches

The relationship between the apothem, 'a', and the circumradius, 'R', is given as follows;

$a = R \cdot cos \left(\dfrac{\pi}{n} \right)$

Where;

n = The number of sides of the regular polygon = 6 for a hexagon

'a = 6·√3 inches', and 'R' are the apothem and the circumradius respectively;

Part A

Therefore, we have;

$The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}$

Plugging in the values gives;

$The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12$

The circumradius, R = 12 inches

Part B

The length of each side of the hexagon, 's', is given as follows;

$s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)$

Therefore, we get;

$s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12$

The length of each side of the hexagon, s = 12 inches

The perimeter of the hexagon, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon = 72 inches

5 0

3 years ago

How much?Please help me.

aniked [119]

Answer:

imma say $5300

Step-by-step explanation: if right plz mark as brainliest

sorry if wrong

8 0

3 years ago

Trinity runs 147 meters in 35 seconds assuming her speed constant: a. write an equation for Trinitys distance, d, in terms of th

noname [10]

Answer:

nb

Step-by-step explanation:

3 0

3 years ago

Multiply the binomials (5x+3) And (2x+4)

Sav [38]

Answer:

(5x+3)(2x+4)=10x^2+26x+12

Step-by-step explanation:

You use FOIL (First, Outer, Inner Last)

First: 5x times 2x= 10x^2

Outer: 5x times 4= 20x

Inner: 3 times 2x= 6x

Last= 3 times 4

Combine 20x and 2x to get 26x

3 0

3 years ago

Hello,..... I will mark you as a brainliest

madam [21]

Answer:

5 jumps

Step-by-step explanation:

Personally I would write it out, although there surely is a formula for it.

3 fall to 2 - 5 fall to 4 - 7 fall to 6 - 10 fall to 9 - 12.

This makes 5 jumps, since once he is out he won't fall back in.

8 0

3 years ago