The lateral surface area of the solid is 655 cm².
Step 1: Identify the lateral faces
The lateral faces of the solid are the four rectangular faces and the two triangular faces.
Step 2: Calculate the area of each lateral face
Rectangular faces: Each rectangular face has dimensions of 20 cm x 8 cm. Area = 20 cm x 8 cm = 160 cm²
Since there are four rectangular faces, the total area of the rectangular faces is 4 x 160 cm² = 640 cm².
Triangular faces: Each triangular face has a base of 5 cm and a height of 3 cm. Area = (1/2)(5 cm)(3 cm) = 7.5 cm²
Since there are two triangular faces, the total area of the triangular faces is 2 x 7.5 cm² = 15 cm²
Step 3: Add the areas of all lateral faces
Total lateral surface area = Area of rectangular faces + Area of triangular faces
Total lateral surface area = 640 cm² + 15 cm² = 655 cm²
Therefore the lateral surface area of the solid is 655 cm².