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Rectangular Parallelepiped Formula

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A Rectangular Parallelepiped is a polyhedron with six faces. Here each face is a rectangle. It can also be called a cuboid. It is a three dimensional (3D) figure. For any two dimensional or three-dimensional figures, the concept of mensuration is applied. Mensuration is the branch of geometry that deals with measurements like length, height, area, volume in 2D/3D figures. It includes the computation of mathematical formulas and algebraic expressions.

Surface Area of a Rectangular Parallelepiped figure

In the Rectangular Parallelepiped figure, there are six rectangles. To determine the surface area of it we need to find the area of six rectangles (faces). The formula for the surface area is given by

Surface Area = 2(l×h) + 2(l×w) + 2(h×w)

S = 2[(l×h) + (l×w) + (h×w)]

where 

l, w, h are length, width, height respectively.

Lateral Surface Area of Rectangular Parallelepiped figure

Lateral Surface Area can be defined as the product of perimeter of base and height. In a rectangular parallelepiped figure, each face is a rectangle so the perimeter of the base is equal to the perimeter of rectangle. The formula for LSA (Lateral surface area) is given by

LSA = Perimeter of base × Height

As perimeter of base is equal to 2(length+width)

= 2(length + width) × Height

LSA = 2lh + 2wh

where

l, w, h are length, width and height respectively.

From the above formula, It can also be said that

Surface Area (Total) = Lateral surface area + 2lw

Volume of Rectangular Parallelepiped figure

The volume of rectangular parallelepiped can be defined as the product of the area of the base and height. As each face in a rectangular parallelepiped is rectangle, the base is also a rectangle and the area of base is the product of length and width. The formula for volume is given by-

Volume = area of base × height

V = l × w × h

Diagonal length of Rectangular Parallelepiped figure

The length of diagonal of rectangular parallelepiped figure with length l, width w and height h can be calculated by the below formula-

[Tex]Diagonal\ length=\sqrt{l^2+w^2+h^2}[/Tex]

Let’s look into couple of questions based on Rectangular Parallelepiped Figure:

Sample Questions

Question 1: What is the surface area of Rectangular Parallelepiped with length 6cm, width 3cm and height 2cm.

Solution:

Given

length(l) = 6cm

width(w) = 3cm

height(h) = 2cm

Surface Area = 2[(l×h)+(l×w)+(h×w)]

= 2[(6×2)+(6×3)+(2×3)]

= 2[12+18+6]

= 2×36

= 72 sq.cm

So, Surface area for the given figure is 72 sq.cm

Question 2: Find the surface area of the Rectangular Parallelepiped figure with length, width and height is 7cm, 5cm, 3cm respectively.

Solution:

Given

length(l) = 7cm

width(w) = 5cm

height(h) = 3cm

Surface Area = 2[(l×h)+(l×w)+(h×w)]

= 2[(7×3)+(7×5)+(3×5)]

= 2[21+35+15]

= 2×71

= 142 sq.cm

So, Surface area for the given figure is 142 sq.cm

Question 3: What is the lateral surface area of Rectangular Parallelepiped with length 6cm, width 3cm and height 2cm.

Solution:

Given

length(l) = 6cm

width(w) = 3cm

height(h) = 2cm

Lateral Surface Area = 2(l+w)×h

= 2(6+3)×3

= 2(9)×3

= 18×3

= 54 sq.cm

So, Lateral Surface area for the given figure is 54 sq.cm

Question 4: What is the volume of rectangular parallelepiped figures if the measurements such as length, width and height are 4cm, 3cm, 2cm respectively.

Solution:

Given,

length(l) = 4cm

width(w) = 3cm

height(h) = 2cm

volume = l × w × h

= 4 × 3 × 2

= 24cm3

Volume of given rectangular parallelepiped figure is 24cm3.

Question 5: Find the volume of rectangular parallelepiped figure if the length is 5cm, width is 4cm and height is 4cm.

Solution:

Given,

length(l) = 5cm

width(w) = 4cm

height(h) = 4cm

volume = l × w × h

= 5 × 4 × 4

= 80cm3

Volume of given rectangular parallelepiped figure is 80cm3.

Question 6: Find the volume of rectangular parallelepiped figure if the length is 5cm, width is 4cm and height is 2cm.

Solution:

Given,

length(l) = 5cm

width(w) = 4cm

height(h) = 2cm

Diagonal length = [Tex]\sqrt{l^2+w^2+h^2}[/Tex]

= [Tex]\sqrt{5^2+4^2+2^2}[/Tex]

= [Tex]\sqrt{25+16+4}[/Tex]

= [Tex]\sqrt{45}[/Tex]

= 6.7 cm

Diagonal length of given rectangular parallelepiped figure is 6.7cm.

Question 7: Find the volume of rectangular parallelepiped figures if the length, width and height are 4cm, 2cm and 0.5cm respectively.

Solution:

Given,

length(l) = 4cm

width(w) = 2cm

height(h) = 0.5cm

Diagonal length = [Tex]\sqrt{l^2+w^2+h^2}[/Tex]

= [Tex]\sqrt{4^2+2^2+(0.5)^2}[/Tex]

= [Tex]\sqrt{16+4+0.25}[/Tex]

= [Tex]\sqrt{20.25}[/Tex]

= 4.5 cm

Diagonal length of given rectangular parallelepiped figure is 4.5cm.



Last Updated : 18 Feb, 2024
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