Question

How do you find the area of the lateral side?

Answer 1

We use the formula of lateral surface area of rectangular prism. Compare the given figure with rectangular prism and write the dimensions of length, breadth and height of the figure. Calculate the lateral surface area using the perimeter of the base and height of the rectangular prism.

• A rectangular prism is a 3D shape which has six rectangular faces.
• Lateral surface area of any 3D figure is the area of the figure excluding the area of the base and the top of the 3D figure.

Complete step by step answer: We are given the figure of a rectangular prism.
Since we know rectangular prism has length, breadth and height, comparing the measurements of given figure we can write
Length of rectangular prism, $l = 3$cm
Breadth of the rectangular prism, $b = 2$cm
Height of the rectangular prism, $h = 6$cm
Now we know the lateral surface area is the area of the figure excluding the area of the base.
We can write the formula for lateral surface area of the rectangular prism as perimeter of base multiplied by height of the rectangular prism.
$\Rightarrow$L. S. A of rectangular prism $= \left( {l + b + l + b} \right) \times h$
Add the same terms in the bracket
$\Rightarrow$L. S. A of rectangular prism $= 2\left( {l + b} \right) \times h$
Substitute the value of length, breadth and height in the formula of lateral surface area of rectangular prism.
$\Rightarrow$L. S. A of rectangular prism = \left( {2\left( {3 + 2} \right) \times 6} \right)$$$$c{m^2}
Add the terms in the bracket
$\Rightarrow$L. S. A of rectangular prism = \left( {2\left( 5 \right) \times 6} \right)$$$$c{m^2}
Multiply the term inside the bracket with the term outside the bracket
$\Rightarrow$L. S. A of rectangular prism = \left( {10 \times 6} \right)$$$$c{m^2}
$\Rightarrow$L. S. A of rectangular prism = 60$$$$c{m^2}
$\therefore$Lateral surface area of the given figure is 60 $c{m^2}$.

Note:
Many students make the mistake of calculating the lateral surface area wrong as they write the formula as area of base multiplied with height which is wrong. Keep in mind the word lateral means the sum of the area of all sides of a 3D object i.e. we exclude base and top from the area and if we mount the perimeter of base till we reach the height we can form the sides of the 3D object.