Surface area of rectangular prism is the measure of how much exposed area a solid object has, expressed in square units.
All the faces of a Rectangular prism are rectangular. This makes calculating the areas of these surfaces very easily. The area of Rectangle have been discussed in another section, which is available for review before proceeding, if necessary. There are 6 faces in rectangular prism so to find the surface area of rectangular prism , add the area of each face.
If the Rectangular prism is open from top and bottom then its area is called Area of 4 walls or Lateral surface area.
Formulas for surface area of rectangular prism :
Surface area = 2 ( lw + wh + lh)
Lateral surface area = 2h (l + w)
Length of diagonal = √( l^{2} + w^{2} + h^{2})
Some solved examples on surface area of rectangular prism
1) A rectangular box of length 40 cm, width 25 cm and height 20 cm is to be made of tin. What is the area of tin sheet required if the box has a lid also? Solution : l = 40 cm ; w = 25 cm and h = 20 cm
Total surface area of box = 2 ( l x w + w x h + l x h)
Area = 2 ( 40 x 25 + 25 x 20 + 40 x 20 )
= 2 ( 1000 + 500 + 800 )
= 2 x 2300
Area = 4600 cm^{2}
________________________________________________________________
2) A rectangular room of dimensions 8 m x 6 m x 3 m is to be painted. If it costs $60 per square meter, find the cost of painting the walls of the room. Solution : l = 8 m ; w = 6 m ; h = 3 m
Painting walls of the room that means here we have to use the formula for area of 4 walls.
Area of 4 walls = 2 x h (l + w)
= 2 x 3 ( 8 + 6)
= 6 x 14
Area of walls = 84 m^{2}
Cost of painting 4 walls = 84 x 60 = $ 5040
________________________________________________________________
3) The sum of length, width and depth(height) of a rectangular box is 19 cm and length of its diagonal is 11 cm. Find the surface area of the box. Solution : l + w + h = 19
Diagonal = 11 cm
⇒ &radi; ( l^{2} + w^{2} + h^{2}) = 11
⇒ l^{2} + w^{2} + h^{2} = 121
l + w + h = 19
⇒ ( l + w + h)^{2} = 19^{2}
⇒ l^{2} + w^{2} + h^{2} + 2( lw + wh + lh) = 361
⇒ 121 + 2 (lw + wh + lh) = 361
⇒ 2(lw + wh + lh ) = 240
Hence, the surface area of box is 240 m^{2}
_________________________________________________________________
4) The length and width of a hall are in the ratio 4:3 and its height is 5.5 m. The cost of decorating its walls (including doors and windows ) at $ 6.60 per square meter is $5082. Find the length and width of the room. Solution :
As the cost of decorating walls is $ 5082 at the rate of $ 6.60 per square meter.
∴ Area of walls = 5082 / 6.60 = 770 m^{2}
Let x be the ratio.
Length = 4x and width = 3x
Height = h = 5.5 m
Area of walls = 2 h ( l + w)
770 = 2 x 5.5 ( 4x + 3x )
770 = 11 ( 7x)
∴ 7x = 770 / 11
⇒ 7x = 70
⇒ x = 10
∴ length = 4x = 4(10) = 40 m and width = 3x = 3(10) = 30 m. Surface Area :