Calculate the shaded area of the shaded region in the figure below.

$$A_{nje} = \text{urefu} \times \text{upana} = 28 \text{ cm} \times 20 \text{ cm}$$ $$A_{nje} = 560 \text{ cm}^2$$

$$A_{ndani} = \text{urefu} \times \text{upana} = 24 \text{ cm} \times 10 \text{ cm}$$ $$A_{ndani} = 240 \text{ cm}^2$$

Eneo lililotiwa kivuli = Eneo la mstatili wa nje - Eneo la mstatili wa ndani

$$A_{kivuli} = 560 \text{ cm}^2 - 240 \text{ cm}^2$$ $$\boxed{\text{Eneo lililotiwa kivuli} = \textbf{320 cm}^2}$$

Mchoro wa Pili (Juu kulia):
Mraba wenye duara ndani yake.
Urefu wa upande wa mraba ni $14 \text{ cm}$.
Kipenyo cha duara ni $14 \text{ cm}$, hivyo rediasi ni $r = \frac{14}{2} = 7 \text{ cm}$.

$$A_{mraba} = \text{upande}^2 = (14 \text{ cm})^2$$ $$A_{mraba} = 196 \text{ cm}^2$$

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

$$A_{duara} = \pi r^2 = \frac{22}{7} \times (7 \text{ cm})^2$$ $$A_{duara} = \frac{22}{7} \times 49 \text{ cm}^2$$ $$A_{duara} = 22 \times 7 \text{ cm}^2 = 154 \text{ cm}^2$$

Eneo lililotiwa kivuli = Eneo la mraba - Eneo la duara

$$A_{kivuli} = 196 \text{ cm}^2 - 154 \text{ cm}^2$$ $$\boxed{\text{Eneo lililotiwa kivuli} = \textbf{42 cm}^2}$$

Mchoro wa Tatu (a) (Katikati kushoto):
Umbo la pete (annulus) lenye duara mbili zenye kituo kimoja.
Rediasi ya duara kubwa ni $R = 14 \text{ cm}$.
Rediasi ya duara ndogo ni $r = 7 \text{ cm}$.

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

$$A_{kubwa} = \pi R^2 = \frac{22}{7} \times (14 \text{ cm})^2$$ $$A_{kubwa} = \frac{22}{7} \times 196 \text{ cm}^2$$ $$A_{kubwa} = 22 \times 28 \text{ cm}^2 = 616 \text{ cm}^2$$

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

$$A_{ndogo} = \pi r^2 = \frac{22}{7} \times (7 \text{ cm})^2$$ $$A_{ndogo} = \frac{22}{7} \times 49 \text{ cm}^2$$ $$A_{ndogo} = 22 \times 7 \text{ cm}^2 = 154 \text{ cm}^2$$

Eneo lililotiwa kivuli = Eneo la duara kubwa - Eneo la duara ndogo

$$A_{kivuli} = 616 \text{ cm}^2 - 154 \text{ cm}^2$$ $$\boxed{\text{Eneo lililotiwa kivuli} = \textbf{462 cm}^2}$$

Mchoro wa Nne (Katikati kulia):
Mstatili wenye duara ndani yake.
Urefu wa mstatili ni $15 \text{ cm}$ na upana ni $12 \text{ cm}$.
Kipenyo cha duara ni $14 \text{ cm}$, hivyo rediasi ni $r = \frac{14}{2} = 7 \text{ cm}$.

$$A_{mstatili} = \text{urefu} \times \text{upana} = 15 \text{ cm} \times 12 \text{ cm}$$ $$A_{mstatili} = 180 \text{ cm}^2$$

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

$$A_{duara} = \pi r^2 = \frac{22}{7} \times (7 \text{ cm})^2$$ $$A_{duara} = \frac{22}{7} \times 49 \text{ cm}^2$$ $$A_{duara} = 22 \times 7 \text{ cm}^2 = 154 \text{ cm}^2$$

Eneo lililotiwa kivuli = Eneo la mstatili - Eneo la duara

$$A_{kivuli} = 180 \text{ cm}^2 - 154 \text{ cm}^2$$ $$\boxed{\text{Eneo lililotiwa kivuli} = \textbf{26 cm}^2}$$