Question

find the area of the shape. either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.

Explanation:

Step1: Identify shape and formula

The shape is a quarter-circle (90° sector, 1/4 of a full circle). The area of a full circle is $A_{full} = \pi r^2$, so the quarter-circle area is $\frac{1}{4} \pi r^2$.

Step2: Substitute radius $r=2$

Substitute $r=2$ into the quarter-circle area formula:
$\text{Area} = \frac{1}{4} \pi (2)^2$

Step3: Simplify exact form

Calculate $(2)^2=4$, then $\frac{1}{4} \times 4 = 1$, so exact area is $\pi$.

Step4: Calculate decimal form

Use $\pi=3.14$: $\text{Area} = 3.14$

Answer:

Exact answer: $\pi$
Decimal answer: $3.14$