Calculate the area of the unshaded region in the figure below. 2) Calculate the shaded area of shaded region in the figure below.

$$A_{mkubwa} = \text{urefu} \times \text{upana} = 36 \text{ cm} \times 25 \text{ cm}$$ $$A_{mkubwa} = 900 \text{ cm}^2$$

$$A_{kivuli} = \text{urefu} \times \text{upana} = 20 \text{ cm} \times 18 \text{ cm}$$ $$A_{kivuli} = 360 \text{ cm}^2$$

Eneo lisilo na kivuli = Eneo la mstatili mkubwa - Eneo la mstatili wenye kivuli

$$A_{isiyo\_kivuli} = 900 \text{ cm}^2 - 360 \text{ cm}^2$$ $$\boxed{\text{Eneo lisilo na kivuli} = \textbf{540 cm}^2}$$

Swali la 2b: Kokotoa eneo lililotiwa kivuli katika mchoro hapa chini.
Mchoro unaonyesha mraba wenye nusu duara ndani yake. Sehemu iliyotiwa kivuli ni ile iliyo ndani ya mraba lakini nje ya nusu duara.
Kutokana na gridi, tunaweza kudhani upande wa mraba ni $4 \text{ cm}$.
Kipenyo cha nusu duara ni sawa na upande wa mraba, hivyo kipenyo ni $4 \text{ cm}$.
Rediasi ya nusu duara ni $r = \frac{4}{2} = 2 \text{ cm}$.

$$A_{mraba} = \text{upande}^2 = (4 \text{ cm})^2$$ $$A_{mraba} = 16 \text{ cm}^2$$

(Tumia $\pi = \frac{22}{7}$)

$$A_{nusu\_duara} = \frac{1}{2} \pi r^2 = \frac{1}{2} \times \frac{22}{7} \times (2 \text{ cm})^2$$ $$A_{nusu\_duara} = \frac{1}{2} \times \frac{22}{7} \times 4 \text{ cm}^2$$ $$A_{nusu\_duara} = \frac{44}{7} \text{ cm}^2 \approx 6.2857 \text{ cm}^2$$

Eneo lililotiwa kivuli = Eneo la mraba - Eneo la nusu duara

$$A_{kivuli} = 16 \text{ cm}^2 - \frac{44}{7} \text{ cm}^2$$ $$A_{kivuli} = \frac{16 \times 7 - 44}{7} \text{ cm}^2 = \frac{112 - 44}{7} \text{ cm}^2$$ $$A_{kivuli} = \frac{68}{7} \text{ cm}^2$$ $$\boxed{\text{Eneo lililotiwa kivuli} = \textbf{9.71 cm}^2 \text{ (kwa sehemu mbili za desimali)}}$$