Question

Find the lateral surface area and total surface area of the following right prisms.

Answer 1

Hint: Here we will use the lateral surface area and the total surface area of the prism by using the formula. Lateral surface area can be defined as $ 2h(l + b) $ and total surface area of the prism can be defined as $ 2(lb + bh + hl) $

Complete step by step solution:
Here, we are given the measures of the prism as,
Height, $ h = 5cm $
Breadth, $ b = 6cm $
Length, $ l = 8cm $
Now, the lateral surface area $ = 2h(l + b) $
Place the values in the above equation-
Lateral Surface area $ = 2(5)(6 + 8) $
Simplify the above equation –
Lateral Surface area $ = 10(14) $
Find the value finding the product of the terms on the right hand side of the equation.
Lateral Surface area $ = 140\,{\text{c}}{{\text{m}}^2} $ ….. (A)
Now, the total surface area of the prism is $ = 2(lb + bh + hl) $
Place the values in the above equation-
Total surface area of the prism is $ = 2[8(6) + 6(5) + 5(8)] $
Simplify the above equation –
Total surface area of the prism is $ = 2[48 + 30 + 40] $
Simplify the above expression finding the sum of the terms inside the bracket and then multiply with the term outside the bracket.
Total surface area of the prism is $ = 2[118] $
Total surface area of the prism is $ = 236\;c{m^2} $ …. (B)
Equation (A) and (B) are the required solutions.

Note: Know the difference between the lateral surface area and the total surface area of the prism. Always remember to write the relevant units to the resultant values of the areas. Always remember the difference between the area and perimeter. Area is the inside space or the region whereas the perimeter is the outer edge or the surface. Area is measured in square units whereas perimeter in units such as meter, centimetre. Do not forget to write the appropriate unit after the solution.