Need help quickly very confused!

Question

A regular hexagonal prism has an edge length 12 cm, and height 10 cm. Identify the volume of the prism to the nearest tenth.

A.) V = 1870.6 cm³

B.) V = 2776.2 cm³

C.) V = 3741.2 cm³

D.) V = 7482.5 cm³

Need help very quickly!

Answer 1

C.. 3741.2

Volume = (Area of Base)*Height

Hexagon is 6 equal triangles:

Each triangle has a base length of 12 cm.

What is the height of this triangle. (Note not the same height as the prism)

_ 12cm _ _

\ | / Angle C

\ | /

\ | /

\ | /

\ | /

\|/ Angle A

Angle A is 360 degrees divided by 6 (# of triangles) which is 60 degrees. Now as seen in the picture we have to divide A in half to determine the height and divide length A (12 cm) in half. Angle C is 60 degrees since all angles in a triangle equal 180.

Sin A/A=SinC/C Sin(30)/6=Sin(60)/C solve for C C=6*sin(60)/sin(30) C= 10.3923

Now the area of each triangle = 0.5*base*height = 0.5*12cm*10.3923 cm =62.3538 cm²

Six Triangles (the base of the hexagon) =374.12 cm²

Volume of Prism = base* height =374.12 cm²* 10 cm

Volume = 3741.2 cm³

Answer 2

V = Bh

B = 3√3/2(12^2) = 374.12

Move the decimal over one.

C