Question

A dinner platter is in the shape of a regular decagon. The platter has an area of 161 square inches and a side length of 4.6 inches. What is the area of each triangle? What is the height of each triangle?

Answer 1

When I saw this, I said to myself  "Self !  We don't know anything about
decagons.", and then I went searching online for stuff about decagons.
This just goes to show how stupid I can be when I don't take a little time
to THINK before I go running around screaming.

-- When you draw all the lines from the center to the vertices of the
decagon, you'll have 10 little triangles.

-- The area of the whole thing is 161 square inches, so the area of each
little triangle is 1/10 of that . . . . . 16.1 square inches.

-- The area of each little triangle is  (1/2) (base) (height), just like
every other triangle.
The base is the 4.6 inches of one side of the decagon.
              
                                                  Area = (1/2) (base) (height)

Multiply each side by 2:         2 x area = (base) x (height)

Divide each side by (base):  (2 x area) / (base) = height

                              Height = (2 x 16.1) / (4.6) =  7 inches .

Let that be a lesson to both of us.
THINK before you jump.