Finding the area of the region bounded by the graphs of $y=|x|$, $y=|x|+3$, and $y=5-|x|$

Question

Find the area of the region bounded by the graphs of $y = |x|$, $y = |x| + 3$, and $y = 5 - |x|$.

I got $\left(\dfrac{5\sqrt2}2\right)^2$, but this is incorrect.

I don't really understand what the problem means when they say "bounded" because there is a small region, and a big region that could both be interpreted as the "bounded region."

Any solution + clarification on what this bounded region is? Thanks.

Answer 1

I think it's the area of the square bounded by $(0,0), (\dfrac52,\dfrac52), (0,5), $ and $(-\dfrac52,-\dfrac52)$

minus the area of the square bounded by $(0,3),(1,4), (0,5), $ and $(-1,4)$.

(That small square is bounded by only two of the three graphs.)

The area of a square with diagonal length $d$ is $\dfrac{d^2}2$.

Can you use this information to get the correct answer?

Answer 2

The region is bounded by each of the three graphs. It is yellow in the enclosed picture.