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.

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: $A_{full} = \pi r^2$, $r=6$.
$A_{full} = \pi \times 6^2 = 36\pi$

Step3: Compute shape area

Multiply full area by $\frac{3}{4}$.
$A = \frac{3}{4} \times 36\pi = 27\pi$

Step4: Decimal conversion (optional)

Substitute $\pi=3.14$:
$A = 27 \times 3.14 = 84.78$

Answer:

Exact answer: $27\pi$
Decimal answer: $84.78$