Hello, magentarita!

Let = side of the triangle.A wire 10 meters long is to be cut into two pieces. One piece will be bent

into an equilateral triangle and the other piece will be bent into a circle.

(a) Express the total area enclosed by the pieces of wire as a function

of the length of a side of the equilateral triangle.

The area of an equilateral triangle of side is: .

The triangle uses of the wire.

This leaves for the circumference of the circle.

Circumference formula: .

So we have: .

Area formula: .

So we have: .

Therefore: .

(b) What is the domain of ?

Domain: .