find the surface area:

h=3$ cm. So $A_{\triangle}=\frac{1}{2}\times8\times3=12$ $cm^{2}$. Total area of 2 triangular faces is $2\times12 = 24$ $cm^{2}$.

Step3: Calculate area of first rectangular face

The first rectangle has sides 10 cm and 5 cm. Area $A_{1}=10\times5 = 50$ $cm^{2}$.

Step4: Calculate area of second rectangular face

The second rectangle has sides 10 cm and 8 cm. Area $A_{2}=10\times8=80$ $cm^{2}$.

Step5: Calculate area of third rectangular face

The third rectangle has sides 10 cm and $\sqrt{3^{2}+4^{2}} = 5$ cm (using Pythagorean theorem for the slant - height of the triangle with legs 3 cm and 4 cm). Area $A_{3}=10\times5 = 50$ $cm^{2}$.

Step6: Sum up all areas

$A = 24+50 + 80+50=204$ $cm^{2}$.

Answer:

$204$ $cm^{2}$