The base of a solid right prism is a triangle whose sides are 9cm,12cm and 15 cm.the total surface area of the prism.

not enough information, you didn't give the height of the prism.

Since the base is a right-angled triange, (9^2 + 12^2= 15^2),
the area of the base is (1/2)(9)(12) = 54 cm^2
Once you know the height h, the total surface area would be
2(54) + 9h + 12h + 15h

To find the total surface area of a solid right prism, you must calculate the areas of all its faces and sum them.

1. Start by calculating the area of the triangular base.
- Use Heron's formula to find the area of a triangle with sides a, b, and c.
- Heron's formula:
- Let s = (a + b + c)/2 (semi-perimeter of the triangle)
- Area of the triangle = √(s(s - a)(s - b)(s - c))
- For the given sides of the triangle (9cm, 12cm, and 15cm), calculate the values needed for Heron's formula:
- s = (9 + 12 + 15)/2 = 18
- Area of the triangle = √(18(18 - 9)(18 - 12)(18 - 15))
- Area of the triangle = √(18 * 9 * 6 * 3) = √2916 = 54 cm²

2. Next, calculate the lateral surface area of the prism.
- The lateral surface area is the sum of the areas of the three rectangular faces.
- The formula for the lateral surface area of a right prism is: lateral surface area = perimeter of the base * height
- In this case, the height is not given. We will assume that the height of the prism is the same as the length of the longest side of the base triangle (15 cm).
- Lateral surface area = (perimeter of the triangle base) * (height of the prism)
- Perimeter of the triangle base = 9 + 12 + 15 = 36 cm
- Height of the prism = 15 cm
- Lateral surface area = 36 cm * 15 cm = 540 cm²

3. Finally, calculate the total surface area by summing the triangular base and the lateral surface area.
- Total surface area = area of the base + lateral surface area
- Total surface area = 54 cm² + 540 cm² = 594 cm²

Therefore, the total surface area of the solid right prism is 594 cm².