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$a = \frac{1}{2}r^{2}\theta$
$a = \frac{1}{2}( )^{2}( )$
$a=( )\text{ cm}^2$

Explanation:

Step1: Identify radius and angle values

The radius $r = 4$ cm and the angle $\theta=\frac{5\pi}{4}$ rad.

Step2: Substitute values into formula

$A=\frac{1}{2}(4)^{2}(\frac{5\pi}{4})$

Step3: Simplify the expression

$A=\frac{1}{2}\times16\times\frac{5\pi}{4}=10\pi$

Answer:

$10\pi$