[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-
- Here, we have composite figure which is composed of 2 cuboids.
- The dimensions of larger cuboid is 12cm, 7cm, 7cm
- The dimensions of smaller cuboid is 7cm, 2cm , 2cm
To Find :-
- We have to find the total surface area of the composite figure
Let's Begin :-
Here,
The dimension of larger cuboid are
- Length = 12cm
- Breath = 7 cm
- height = 7 cm
We know that,
Lateral surface area of cuboid
[tex]\bold{\red{ = 2( lb + bh + hl)}}[/tex]
Subsitute the required values,
[tex]\sf{ = 2[(7)(7) + (7)(12) +(7)(12) ]}[/tex]
[tex]\sf{ = 2[ 49 + 84 ]}[/tex]
[tex]\sf{ = 2[ 49 + 168 ]}[/tex]
[tex]\sf{ = 2[ 217 ]}[/tex]
[tex]\bold{ = 434 cm^{2}}[/tex]
Now,
We have to find the lateral surface area of smaller cuboid
- The dimensions of smaller cuboid are 7cm, 2cm and 2cm
Therefore,
Lateral surface area of smaller cuboid
[tex]\sf{ = 2[(2)(7) + (7)(2) +(2)(2) ]}[/tex]
[tex]\sf{ = 2[ 14 + 14 + 4 ]}[/tex]
[tex]\sf{ = 2[ 28 + 4 ]}[/tex]
[tex]\sf{ = 2[ 32]}[/tex]
[tex]\bold{ = 64 cm^{2}}[/tex]
The common base area of both the cuboids
[tex]\sf{ = lb }{\sf{ + lb}}[/tex]
[tex]\sf{ = 14 + }{\sf{ 14}}[/tex]
[tex]\bold{ = 28 cm^{2}}[/tex]
Now,
The total surface area of the given composite figure
= SA of larger cuboid + SA of smaller cuboid - common base area
Subsitute the required values,
[tex]\sf{ = 434 + 64 - 28 }[/tex]
[tex]\sf{ = 498 - 28 }[/tex]
[tex]\bold{ = 470cm^{2}}[/tex]
Hence, The surface area of composite figure is 470 cm² .
