Find the surface area of this triangular prism.Length: 5cm, Base: 12cm, Height: 8cm, Sloping edges: 10cm.

To find the surface area of a triangular prism, you need to find the area of the two triangular faces and the three rectangular faces and add them together.

Step 1: Find the area of the triangular faces. The area of a triangle is 1/2 * base * height. In this case, the base is 12 cm and the height is 8 cm. So, the area of one triangle is 1/2 * 12 cm * 8 cm = 48 square cm. Since there are two triangular faces, the total area of the triangular faces is 2 * 48 square cm = 96 square cm.

Step 2: Find the area of the rectangular faces. The area of a rectangle is length * width. The three rectangular faces have dimensions 5 cm by 12 cm, 5 cm by 8 cm, and 5 cm by 10 cm. So, their areas are 5 cm * 12 cm = 60 square cm, 5 cm * 8 cm = 40 square cm, and 5 cm * 10 cm = 50 square cm.

Step 3: Add the areas of all the faces together. The total surface area of the prism is the sum of the areas of all the faces. So, the total surface area is 96 square cm (from the triangular faces) + 60 square cm + 40 square cm + 50 square cm (from the rectangular faces) = 246 square cm.

So, the surface area of the triangular prism is 246 square cm.