(Sleepy)Hello, Gedalas!

I am trying to help my grandfather who is a making a model sailboat.

The sails are isosceles triangles with a curve along the largest edge.

He needs the area in square inches of the sails.

I have found the area of the triangles themselves, but i can't seem to come up with

a method of getting the area of the curved part, which is basically a circle segment.

The only information i have on them is the length of the chord

. . and the distance between the chord and the arc.

. . Length of chord: 54 in.

. . Distance to arc: 2 in.

I will assume that the circular arc is outside the isosceles triangle.

Code:

C
* * *
* |2 *
* | *
A * - - - - - - + - - - - - - * B
\ 27 |D 27 /
\ | /
\ | /
\ | /
\ | /
R \ |R-2 / R
\ | /
\ | /
\ | /
\ | /
\ | /
\ | /
\|/
*
O

We are given: .

Let the radius be

. . Then: .

. . And: .

In right triangle

. .

Hence, the radius is: .

In , apply the Law of Cosines:

. .

. .

The area of sector is:

. .