Answer :
To find the lateral area of a regular prism with a pentagonal base, you'll need to follow these steps:
1. Determine the perimeter of the pentagonal base:
- A regular pentagon has five equal sides. Given that each side length is 6 cm, you can calculate the perimeter of the pentagon by multiplying the side length by the number of sides.
[tex]\[ \text{Perimeter} = 5 \times \text{side length} \][/tex]
Since the side length is 6 cm:
[tex]\[ \text{Perimeter} = 5 \times 6 = 30 \text{ cm} \][/tex]
2. Calculate the lateral surface area of the prism:
- The lateral surface area of a prism is given by the product of the perimeter of the base and the height of the prism. Since the height \( h \) is given as 15 cm, you can use the calculated perimeter.
[tex]\[ \text{Lateral Area} = \text{Perimeter} \times \text{Height} \][/tex]
Using the values we have:
[tex]\[ \text{Lateral Area} = 30 \text{ cm} \times 15 \text{ cm} = 450 \text{ cm}^2 \][/tex]
3. Conclusion:
- The perimeter of the pentagonal base is 30 cm.
- The lateral area of the prism is 450 cm².
Hence, the lateral area of the prism is [tex]\( 450 \, \text{cm}^2 \)[/tex].
1. Determine the perimeter of the pentagonal base:
- A regular pentagon has five equal sides. Given that each side length is 6 cm, you can calculate the perimeter of the pentagon by multiplying the side length by the number of sides.
[tex]\[ \text{Perimeter} = 5 \times \text{side length} \][/tex]
Since the side length is 6 cm:
[tex]\[ \text{Perimeter} = 5 \times 6 = 30 \text{ cm} \][/tex]
2. Calculate the lateral surface area of the prism:
- The lateral surface area of a prism is given by the product of the perimeter of the base and the height of the prism. Since the height \( h \) is given as 15 cm, you can use the calculated perimeter.
[tex]\[ \text{Lateral Area} = \text{Perimeter} \times \text{Height} \][/tex]
Using the values we have:
[tex]\[ \text{Lateral Area} = 30 \text{ cm} \times 15 \text{ cm} = 450 \text{ cm}^2 \][/tex]
3. Conclusion:
- The perimeter of the pentagonal base is 30 cm.
- The lateral area of the prism is 450 cm².
Hence, the lateral area of the prism is [tex]\( 450 \, \text{cm}^2 \)[/tex].
