Introduction :
The prisms are the shapes that exist in the three dimensions. All the prisms are formed by the two bases and the bases of the prism formed by the faces of the prism. Regular polygons form the bases of a prism. In the following article we will discuss more about the online Volume of Right Prism help in detail.
More about the Topic these Form the Bases of a Prism
As we described before the prisms are the shapes formed by the two bases the upper base and the lower bases. All bases of the prism are the regular polygons and these form the bases of the prism. In the right regular prisms the bases of the prism are equal. The area of the bases is calculated as the product of the perimeter fo the base and the height of the prism. And the Formula for the area of the bases of the prism and the area of the total prism including the faces of the prism with the base made of n sides and side length S are,
Area of a base of the prism = `[n*S^2*cot (pi/n)]/4`
Total surface area = `[n*S^2*cot (pi/n)]/2 + S*H*n`
Example Problems on these Form the Bases of a Prism:
1. Calculate area of the base and the total area of the hexagonal prism with the height 10cm and side length of the base 5cm.
Solution:
Area of a base of the prism `= [n*S^2*cot (pi/n)]/4`
`= [6*5^2*cot (pi/5)]/4`
`= 43 cm^2`
Total surface area `= [n*S^2 cot (pi/n)]/2 + S*H*n `
`= [6*5^2*cot (pi /6)]/2 + 6*5*10`
`= (48*1.732) + 300`
`= 129.93 + 300`
`= 429.93 cm^2`
Practice problems on these form the bases of a prism:
1. Calculate area of the base and the total area of the pentagonal prism with the height 10 cm and side length of the base 6cm.
Answer: Total surface area = 423.9 cm2 and Area of a base= 61.94 cm2.
2. Calculate area of the base and the total area of the octagonal prism with the height 9cm and side length of the base 3cm.
Answer: Total surface area = 302.9 cm2 and Area of a base = 43.46 cm2.
The prisms are the shapes that exist in the three dimensions. All the prisms are formed by the two bases and the bases of the prism formed by the faces of the prism. Regular polygons form the bases of a prism. In the following article we will discuss more about the online Volume of Right Prism help in detail.
As we described before the prisms are the shapes formed by the two bases the upper base and the lower bases. All bases of the prism are the regular polygons and these form the bases of the prism. In the right regular prisms the bases of the prism are equal. The area of the bases is calculated as the product of the perimeter fo the base and the height of the prism. And the Formula for the area of the bases of the prism and the area of the total prism including the faces of the prism with the base made of n sides and side length S are,
Area of a base of the prism = `[n*S^2*cot (pi/n)]/4`
Total surface area = `[n*S^2*cot (pi/n)]/2 + S*H*n`
Example Problems on these Form the Bases of a Prism:
1. Calculate area of the base and the total area of the hexagonal prism with the height 10cm and side length of the base 5cm.
Solution:
Area of a base of the prism `= [n*S^2*cot (pi/n)]/4`
`= [6*5^2*cot (pi/5)]/4`
`= 43 cm^2`
Total surface area `= [n*S^2 cot (pi/n)]/2 + S*H*n `
`= [6*5^2*cot (pi /6)]/2 + 6*5*10`
`= (48*1.732) + 300`
`= 129.93 + 300`
`= 429.93 cm^2`
Practice problems on these form the bases of a prism:
1. Calculate area of the base and the total area of the pentagonal prism with the height 10 cm and side length of the base 6cm.
Answer: Total surface area = 423.9 cm2 and Area of a base= 61.94 cm2.
2. Calculate area of the base and the total area of the octagonal prism with the height 9cm and side length of the base 3cm.
Answer: Total surface area = 302.9 cm2 and Area of a base = 43.46 cm2.
