Cut the wire into two lengths, $x$ and $L-x$. Fashion the triangle from the piece of length $x$, and the circle from the piece of length $L-x$.

Figure 3.8.4(a) shows the triangle, the circle, and a graph of the combined area when $L\=10$, wherein the length $x$ is determined by the position of the accompanying slider.

The green dot, synchronized to the slider, traverses the graph of $A\left(x\right)$, the combined areas of the triangle and circle.

From Figure 3.8.4(a), deduce that there is a minimum near $x\=6$ and a maximum at the left endpoint where $x\=0$, that is, when the complete wire is used to fashion the circle.

Control-drag $A\left(x\right)\=\dots$
Context Panel: Assign Function

Write the equation for the critical number;
Press the enter key.

Context Panel: Solve≻Obtain Solutions for≻$x$

Context Panel: Assign to a Name≻$c$ 

Find $A″\left(c\right)\>0$, so $\left(c\,A\left(c\right)\right)$ is a minimum.

From Figure 3.8.5, the absolute maximum occurs when $x\=0$.

Expression palette: Evaluation template
Evaluate $A\left(0\right)$ with $L\=10$

Context Panel: Approximate≻5 (digits)

Expression palette: Evaluation template
Evaluate $c$ with $L\=10$

Context Panel: Approximate≻5 (digits)

Expression palette: Evaluation template
Evaluate $A\left(c\right)$ with $L\=10$ 

Context Panel: Simplify≻Simplify

Context Panel: Approximate≻5 (digits)