A piece of wire 5 inches long is to be cut into two pieces. One peice is x inches long and is to be bent into the shape of a square. The other piece is to be bent into the shape of a circle. Find an expression for the total adrea made up by the square and the circle as a function of x.

Question

aum · Answer

The wire is 5 inches long.  It is cut into two pieces.  
The first piece is "x" inches.  Therefore, the second piece is (5-x) inches.

If you make a square out of a wire that is "x" inches long, what will be the length of each side?

aum · Answer

A square has sides of equal lengths.  Therefore, an "x" inch wire bent into the shape of a square will have each side x/4 inches long.
What is the area of a square when each side is x/4 inches long?

jack1 · Answer

you're doing awesome so far
5 = x + y
x = perimeter of square
y = circumference of circle

$\Large \text {Area of square} = (\frac {\text perimeter}{ 4})^2 $

$ \Large= (\frac x4)^2$

$ \Large= \frac x{16}$

jack1 · Answer

$\Large \text {Area of Circle} = (\pi \times r)^2 $

$\Large Circumference = 2 \times \pi \times r $

$\Large y = 2 \times \pi \times r $

$\Large (5-x) = 2 \times \pi \times r $


$\huge \frac {(5-x)}{2 \pi} =  r $

sub this into the above equation for area of a circle

then total area = sum of both of these shapes area