Final answer:
To find the surface area of the solid with a pentagonal base, calculate the area of the base using the apothem and perimeter, then the area of each lateral face, and add them together. The total surface area is 1640 cm².
Step-by-step explanation:
To calculate the surface area of a solid with a regular pentagonal base where all quadrilaterals are rectangles, we need to calculate the area of the base and the area of the lateral faces separately. First, let's determine the area of the base. The area of a regular pentagon can be calculated by multiplying the perimeter by the apothem and then dividing by 2:
Area of base = ½ × perimeter × apothem = ½ × (5 × s) × a = ½ × (5 × 16) × 11 = 440 cm²
Now, we calculate the surface area of the five rectangular lateral faces. Since all faces are rectangles, the area of each rectangle is the product of its height and side:
Area of one lateral face = l × s = 15 × 16 = 240 cm²
Area of five lateral faces = 5 × 240 cm² = 1200 cm²
Finding the total surface area involves adding the areas of the base and the lateral faces:
Total surface area = Area of base + Area of lateral faces = 440 cm² + 1200 cm² = 1640 cm²
Therefore, the surface area of the solid is 1640 cm².