Answer
$a^{2}$
Work Step by Step
Sketching the function
$f(x)=a-|x|,$ for several values of a, bounds: x=$-a$ to x=$a$.
(see below)
Each value of a produces a triangle, base length $2a$, height $a$,
$A=\displaystyle \frac{1}{2}bh=\frac{1}{2}(2a)a=a^{2}$
$A=\displaystyle \int_{-a}^{a}(a-|x|)dx=a^{2}$
