Okay so- this question is making my brain hurt. The hints I have revived from my instructor are not helpful at all :/ Pls help?

The side length of the regular hexagon is 10 cm. What is the number of square centimeters in the area of the shaded region? Express your answer in simplest radical form.

that's the image D:

tysm in advance!!

Guest Apr 17, 2021

#1**+1 **

Here is my start :

find the measure of the interior angles of the hexagon : there is (6-2)(180) = 720 degrees in the interior angles

720 /6 = 120 degrees

the horizintal dimension of the shaded area is 10

find 'x' =====> the vertical dimension is 2 x can you do it now?

ElectricPavlov Apr 17, 2021

#3**0 **

I've found that the area of the hexagon is 150sqrt(3), but I don't know the height :(

Guest Apr 17, 2021

#4**+1 **

find 'x' (using trig functions that you should know) =====> the vertical dimension is 2 * x

ElectricPavlov
Apr 17, 2021

#7**+1 **

You need the short diagonal ....perhaps that is how you found the answer

short diagonal = sqrt (3) * side length =

sqrt 3 * 10 <====== this is the height of the hexagon

shaded area is then 10 x 10* sqrt 3 cm^{2}

ElectricPavlov
Apr 17, 2021