Question

find the area of the semicircle. either enter an exact answer in terms of \\(\pi\\) or use 3.14 for \\(\pi\\) and enter your answer as a decimal. \\(\square\\) units\\(^2\\)

Explanation:

Step1: Recall full circle area formula

The area of a full circle is $A = \pi r^2$, where $r=14$.

Step2: Calculate full circle area

$A_{full} = \pi (14)^2 = 196\pi$

Step3: Find semicircle area (half full area)

$A_{semicircle} = \frac{1}{2} \times 196\pi = 98\pi$

Step4: (Optional) Decimal approximation

Using $\pi=3.14$, $A_{semicircle} = 98 \times 3.14 = 307.72$

Answer:

Exact answer: $98\pi$ units$^2$
Decimal approximation: $307.72$ units$^2$