A pentagonal prism has a length of 8cm.The area of its pentagonal faces is 43cm2 and the sides of the pentagons are each 5cm.Find its surface area.

To find the surface area of a pentagonal prism, we need to calculate the area of both the pentagonal faces and the rectangular faces.

1. The area of the pentagonal faces is given as 43 cm². Since there are two such faces, their total area is 2 * 43 cm² = 86 cm².

2. To find the area of the rectangular faces, we need to know their dimensions. The length of each rectangle is the same as the length of the prism, 8 cm. The width of each rectangle is the same as the side length of the pentagon, 5 cm. So, the area of one rectangle is 8 cm * 5 cm = 40 cm².

3. Since a pentagonal prism has five rectangular faces, the total area of the rectangular faces is 5 * 40 cm² = 200 cm².

4. Finally, add the area of the pentagonal faces and the rectangular faces to find the total surface area of the prism: 86 cm² + 200 cm² = 286 cm².

So, the surface area of the pentagonal prism is 286 cm².