Calculate the surface area of a triangular prism with a right-angled triangle base (base=5cm, height=10cm) and prism length=25cm.

The prism has a right-angled triangular base.
The base of the triangle is $b = 5 \text{ cm}$.
The height of the triangle is $h = 10 \text{ cm}$.
The length of the prism (depth) is $L = 25 \text{ cm}$.

The area of one triangular base is $A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}$.

Since there are two triangular bases (front and back), their combined area is:

Let the hypotenuse be $c$. Using the Pythagorean theorem:

• The bottom rectangular face has dimensions $5 \text{ cm} \times 25 \text{ cm}$.

• The vertical side rectangular face has dimensions $10 \text{ cm} \times 25 \text{ cm}$.

• The slanted top rectangular face has dimensions $5\sqrt{5} \text{ cm} \times 25 \text{ cm}$.

The total surface area ($TSA$) is the sum of the areas of the two triangles and the three rectangular faces.

To get a numerical value, we approximate $\sqrt{5} \approx 2.236$:

The total surface area is $\text{704.5 cm}^2$.