The diagram below shows a wedge. Determine its total surface area.

Msingi wa pembetatu ni pembetatu ya pembe mraba yenye pande za 6 cm na 8 cm.
Tunatumia theorem ya Pythagoras: $c^2 = a^2 + b^2$.

$$c = \sqrt{6^2 + 8^2}$$ $$c = \sqrt{36 + 64}$$ $$c = \sqrt{100}$$ $$c = 10 \text{ cm}$$

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

$$\text{Eneo la pembetatu moja} = \frac{1}{2} \times 8 \text{ cm} \times 6 \text{ cm} = 24 \text{ cm}^2$$ $$\text{Eneo la pembetatu mbili} = 2 \times 24 \text{ cm}^2 = 48 \text{ cm}^2$$

Urefu wa 'wedge' ni 9 cm.

• Eneo la mstatili wa chini: $8 \text{ cm} \times 9 \text{ cm} = 72 \text{ cm}^2$
• Eneo la mstatili wa upande: $6 \text{ cm} \times 9 \text{ cm} = 54 \text{ cm}^2$
• Eneo la mstatili wa juu uliopinda (hypotenuse $\times$ urefu): $10 \text{ cm} \times 9 \text{ cm} = 90 \text{ cm}^2$

$$\text{Eneo lote la uso} = 48 \text{ cm}^2 + 72 \text{ cm}^2 + 54 \text{ cm}^2 + 90 \text{ cm}^2$$ $$\text{Eneo lote la uso} = 264 \text{ cm}^2$$

Eneo lote la uso wa 'wedge' ni $\text{264 cm}^2$.