What radius of a circle is required to inscribe a regular hexagon with an area of 210.44 cm2 and an apothem of 7.794 cm

1 answer:

8 0

We know that

[area of a regular hexagon]=6*[area of one equilateral triangle]
210.44=6*[area of one equilateral triangle]
[area of one equilateral triangle]=210.44/6-----> 35.07 cm²

[area of one equilateral triangle]=b*h/2
h=7.794 cm
b=2*area/h------> b=2*35.07/7.794------>b= 9 cm

the length side of a regular hexagon is 9 cm
applying the Pythagorean theorem
r²=h²+(b/2)²------>r²=7.794²+(4.5)²------> r²=81--------> r=9 cm

this last step was not necessary because the radius is equal to the hexagon side------> (remember the equilateral triangles)

the answer is
the radius is 9 cm

You might be interested in

Solve for m 3/5m = -15

Mice21 [21]

Answer:

- 25

Step-by-step explanation:

Step 1:

3/5m = - 15 Equation

Step 2:

m = - 15 ÷ 3/5 Divide

Step 3:

m = - 15/1 × 5/3 Multiply

Answer:

m = - 25

Hope This Helps :)

7 0

4 years ago

Read 2 more answers

How fo you solve this equation? 3 3/4 × 9 3/5=

aivan3 [116]

Answer:

Step-by-step explanation:

after converting the mixed numbers to fractions, our initial equation becomes,

15/4 x 48/5

Applying the fractions formula for multiplication,

15 x 48 and 4 x 5 = 720/20

Simplifying 720/20, the answer is 36

6 0

4 years ago

Marcus looked up the path that he had taken on his run this morning on the map shown below.

AURORKA [14]

Answer: 6 miles.

Step-by-step explanation:

1. To solve this problem you only need to add the distances shown in the map attached, which shown the path Marcus had taken. Then, you have:

$Total_{distance}=1in+3inches+2inches+2.3inches\\Total_{distance}=8.3inches$

2. Now, you must convert the result obtained from inches to miles. According to the problem $4inches=3miles$ , therefore, you have:

$Total_{distance}=\frac{8,3inches*3miles}{4inches}\\Total_{distance}=6.22miles$

3. To the nearest mile:

$Total_{distance}=6miles$

6 0

4 years ago

Read 2 more answers

An adult female elephant weighs about 8000 pounds. a newborn baby elephant weighs about 200 pounds. write the ratio of the baby

SIZIF [17.4K]

Answer: 1/40 or .025

See the attached image for the explanation.

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.