Math Is Fun Forum

(a) Prove that one regular hexagon, six squares, and six equilateral triangles, all with the same side length, can be assembled to form a regular dodecagon. (Begin with a diagram of course, but you must also show that at all points where two or more polygons "fit" together, the angles add up to the correct amount.)

(b) The distance between two opposite vertices of the dodecagon is 2. Find the area of the dodecagon.

Please help. I don't know how to start!

A function

has horizontal asymptote of

a vertical asymptote of

and an

-intercept at

Part (a): Let

be of the form

Find an expression for

Part (b): Let

be of the form

Find an expression for

Please don't just give an answer, if you can, please explain.

Suppose that

What is the maximum possible value of

?

Suppose that

What is the maximum possible value of

?

is a square. Parallel lines

,

, and

pass through vertices

,

, and

, respectively. The distance between

and

is 12, and the distance between

and

is 17. Find the area of square

.

I thought because the distances were 12 and 17, I would add them to get 29, the length of the diagonal of ABCD. Then I would just do (29*29)/2 which turned out to be wrong

Let

and

be two

rectangles that overlap, as shown. Find the area of the overlap.

I tried some ideas but turned out to be wrong

ANy help is very much appreciated!

Point G is the midpoint of median

of

. Point

is the midpoint of

, and point

is the intersection of

and

. Find the area of

if

.

I've tried at this problem for a while, and I can't get it. I know many midpoints and that point T seems to be important. Thanks!