Find the requested measurements for the shape below (3 points)

To find the measurements for the shape, we need to calculate the lateral surface area, total surface area, and volume.

1. Lateral Surface Area:
To find the lateral surface area of a triangular prism, we need to calculate the lateral area of the triangle and the area of the rectangular sides.

Area of the triangle = (1/2) * base * height
Area of triangle = (1/2) * 10 cm * 10 cm = 50 cm²

Area of the rectangle = length * height
Area of rectangle = 25 cm * 10 cm = 250 cm²

Lateral Surface Area = Area of triangle + 2 * Area of rectangle
Lateral Surface Area = 50 cm² + 2 * 250 cm² = 550 cm²

2. Total Surface Area:
To find the total surface area of a triangular prism, we need to calculate the sum of the lateral surface area and the area of the two triangular bases.

Total Surface Area = Lateral Surface Area + 2 * Area of triangle
Total Surface Area = 550 cm² + 2 * 50 cm² = 650 cm²

3. Volume:
To find the volume of a triangular prism, we need to calculate the area of the triangular base and then multiply by the height.

Volume = Area of triangle base * height
Volume = 50 cm² * 10 cm = 500 cm³

Therefore, the measurements for the given triangular prism are:
Lateral Surface Area = 550 cm²
Total Surface Area = 650 cm²
Volume = 500 cm³