A circle is inscribed in a square of side 7 cm. Find the area of the circle.

Upande wa mraba ($s$) ni $7 \text{ cm}$.
Kwa duara iliyo ndani ya mraba, kipenyo ($d$) cha duara ni sawa na upande wa mraba.
Hivyo, $d = 7 \text{ cm}$.
Radiasi ($r$) ya duara ni nusu ya kipenyo.

$$r = \frac{d}{2} = \frac{7 \text{ cm}}{2} = 3.5 \text{ cm}$$

Eneo la mraba ($A_{\text{mraba}}$) linapatikana kwa fomula $s^2$.

$$A_{\text{mraba}} = s^2$$ $$A_{\text{mraba}} = (7 \text{ cm})^2$$ $$A_{\text{mraba}} = 49 \text{ cm}^2$$

Eneo la mraba ni $\boxed{\text{49 cm}^2}$.

Eneo la duara ($A_{\text{duara}}$) linapatikana kwa fomula $\pi r^2$. Tutatumia $\pi \approx 3.14159$.

$$A_{\text{duara}} = \pi r^2$$ $$A_{\text{duara}} = \pi (3.5 \text{ cm})^2$$ $$A_{\text{duara}} = \pi (12.25 \text{ cm}^2)$$ $$A_{\text{duara}} \approx 3.14159 \times 12.25 \text{ cm}^2$$ $$A_{\text{duara}} \approx 38.484575 \text{ cm}^2$$

Eneo la duara, likizungushwa hadi sehemu mbili za desimali, ni $\boxed{\text{38.48 cm}^2}$.

Hili linapatikana kwa kutoa eneo la duara kutoka eneo la mraba.

$$A_{\text{iliyobaki}} = A_{\text{mraba}} - A_{\text{duara}}$$ $$A_{\text{iliyobaki}} = 49 \text{ cm}^2 - 38.484575 \text{ cm}^2$$ $$A_{\text{iliyobaki}} \approx 10.515425 \text{ cm}^2$$

Eneo la sehemu iliyobaki, likizungushwa hadi sehemu mbili za desimali, ni $\boxed{\text{10.52 cm}^2}$.