Trig/Geometry-Finding the area

[mcbeth39]

I'm having trouble with these types of problems. I don't know what I'm doing wrong! Please can you point out what mistake(s) I'm making? Thank you.

Find the area of a regular hexagon with side length of 10 centimeters.

Multiple Choice
A 129.9 cm^
B 150 cm^
C 259.8cm^
D 519.6 cm^

 

[Deleted member 4993]

I'm having trouble with these types of problems. I don't know what I'm doing wrong! Please can you point out what mistake(s) I'm making? Thank you.

Find the area of a regular hexagon with side length of 10 centimeters.

Multiple Choice
A 129.9 cm^
B 150 cm^
C 259.8cm^
D 519.6 cm^

The value of x is:

x = 5 * tan(60) = 8.660254038

 

[Mrspi]

I'm having trouble with these types of problems. I don't know what I'm doing wrong! Please can you point out what mistake(s) I'm making? Thank you.

Find the area of a regular hexagon with side length of 10 centimeters.

Multiple Choice
A 129.9 cm^
B 150 cm^
C 259.8cm^
D 519.6 cm^

Ok...you've got that little triangle, with a 30-degree angle at the center of the hexagon. The radius of the hexagon is 10 cm, and that is the HYPOTENUSE of the little triangle. The longer leg is x. The shorter leg is HALF of the hypotenuse (remember? You drew an altitude in the equilateral triangle with sides of 10 cm. That altitude BISECTS the opposite side!).

So, instead of having tan 30 = x/10, it REALLY should be tan 30 = 5/x....tan 30 = opposite leg/adjacent leg
Try that, and see if the value of x you get ultimately produces the right area.

 

[mmm4444bot]

It looks like you incorrectly set up the equation for finding x.

tan(30°) = 5/x

Once you find the height x, the area of each triangle is:

0.5 * 10 * x

(Don't forget that you have six triangles.)

Cheers ~ Mark

 

[mcbeth39]

Thanks guys! That was a silly mistake...

So...

tan 30= x/5

*5 tan 30=x

x= 2.88675

.5 (2.88675) (60)
86.6025*6 = Answer D
YAY!

 

[Deleted member 4993]

Thanks guys! That was a silly mistake...

So...

tan 30= x/5

*5 tan 30=x <<<< That is not correct x = 5*tan(60)

x= 2.88675

.5 (2.88675) (60)
86.6025*6 = Answer D
YAY!

 

[mmm4444bot]

tan 30= x/5

This is not what I wrote!

 

[TchrWill]

I'm having trouble with these types of problems. I don't know what I'm doing wrong! Please can you point out what mistake(s) I'm making? Thank you.

Find the area of a regular hexagon with side length of 10 centimeters.

Multiple Choice
A 129.9 cm^
B 150 cm^
C 259.8cm^
D 519.6 cm^

Hexagon = six equilateral triangles with central angles of 60º

If side length is 10, the other central sides are also 10.

Apothem = 10*cos30º = 8.660

Area = (1/2)(10)(8.660)(6) = 259.8 sq.units