Calculate the surface area of the solid below using its net. Round off to three significant figures.

Pembetatu ya msingi ina pande 10 cm, 10 cm, na 12 cm. Ni pembetatu pacha (isosceles triangle). Tunaweza kutumia theorem ya Pythagoras kupata urefu ($h_t$) wa pembetatu.

$$h_t = \sqrt{10^2 - \left(\frac{12}{2}\right)^2}$$ $$h_t = \sqrt{10^2 - 6^2}$$ $$h_t = \sqrt{100 - 36}$$ $$h_t = \sqrt{64}$$ $$h_t = 8 \text{ cm}$$

Eneo la pembetatu moja ni $\frac{1}{2} \times \text{base} \times \text{height}_t$.

$$\text{Eneo la pembetatu moja} = \frac{1}{2} \times 12 \text{ cm} \times 8 \text{ cm} = 48 \text{ cm}^2$$ $$\text{Eneo la pembetatu mbili} = 2 \times 48 \text{ cm}^2 = 96 \text{ cm}^2$$

Kuna nyuso mbili za mstatili zenye vipimo 10 cm na 8 cm.

$$\text{Eneo la mstatili miwili} = 2 \times (10 \text{ cm} \times 8 \text{ cm}) = 2 \times 80 \text{ cm}^2 = 160 \text{ cm}^2$$

Kuna uso mmoja wa mstatili wenye vipimo 12 cm na 8 cm.

$$\text{Eneo la mstatili mmoja} = 12 \text{ cm} \times 8 \text{ cm} = 96 \text{ cm}^2$$

Eneo la jumla la uso ni jumla ya maeneo yote ya nyuso.

$$\text{Eneo la jumla la uso} = 96 \text{ cm}^2 + 160 \text{ cm}^2 + 96 \text{ cm}^2$$ $$\text{Eneo la jumla la uso} = 352 \text{ cm}^2$$

Eneo la jumla la uso wa mchoro ni $\boxed{\text{352 cm}^2}$.

Sehemu ya 2: Kuzungusha Nambari kwa Tarakimu Tatu Muhimu

a) 4.9852
Tarakimu tatu za kwanza muhimu ni 4, 9, 8. Tarakimu ya nne ni 5, kwa hivyo tunazungusha tarakimu ya tatu (8) kwenda juu.

$$\text{4.9852} \approx \boxed{\text{4.99}}$$

b) 0.078172
Sifuri za mwanzo si muhimu. Tarakimu tatu za kwanza muhimu ni 7, 8, 1. Tarakimu ya nne ni 7, kwa hivyo tunazungusha tarakimu ya tatu (1) kwenda juu.

$$\text{0.078172} \approx \boxed{\text{0.0782}}$$