Answer:
![19.625\text{ cm}^2](https://img.qammunity.org/2021/formulas/mathematics/middle-school/cv1211lxpd8ut6lydye2akmx92prfsr8rm.png)
Explanation:
GIVEN: A square with base
, a circle that perfectly fits inside square.
TO FIND: Approximate area of circle.
SOLUTION:
Consider the figure attached.
let the radius of circle be
![x\text{ cm}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/jtac2dq8t34rkuojtx4wsuhzg3le5ff0c9.png)
radius of circle
![=\frac{\text{length of base of square}}{2}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/tn9wtu70gfm16arz6il3f4i48ysvploi0f.png)
![x=(5)/(2)\text{ cm}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/eagfuu1zsr1z9g15utejmlj4pzsigznp0r.png)
![x=2.5\text{ cm}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/7wzlx6ziidnwvfjy2c5aoytfjjyxqdla0u.png)
Area of circle
![=\pi(radius)^2](https://img.qammunity.org/2021/formulas/mathematics/middle-school/opnyptueotn2szg4bexyq6zeul66dj9cxu.png)
![=3.14*(2.5)^2](https://img.qammunity.org/2021/formulas/mathematics/middle-school/uq6e7xho3aw7axbjvvo03t878kpua4i6i9.png)
![=19.625\text{ cm}^2](https://img.qammunity.org/2021/formulas/mathematics/middle-school/4ar3jxkeairl8tctl5rlgt12ta5e87ue4m.png)
Hence the area of circle that perfectly fits inside the square is
![19.625\text{ cm}^2](https://img.qammunity.org/2021/formulas/mathematics/middle-school/cv1211lxpd8ut6lydye2akmx92prfsr8rm.png)