Question

find the area of the shape. 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: Identify fraction of full circle

The shape is $\frac{3}{4}$ of a full circle (since $360^\circ - 90^\circ = 270^\circ$, $\frac{270}{360}=\frac{3}{4}$).

Step2: Calculate full circle area

Full circle area formula: $A_{full} = \pi r^2$. Here $r=2$, so $A_{full} = \pi (2)^2 = 4\pi$.

Step3: Find shape's area

Multiply full area by $\frac{3}{4}$: $A = \frac{3}{4} \times 4\pi = 3\pi$.

Step4: Decimal approximation (optional)

Substitute $\pi=3.14$: $A = 3 \times 3.14 = 9.42$.

Answer:

Exact answer: $3\pi$ units$^2$
Decimal answer: $9.42$ units$^2$