Question

Pls help. i know the formulas, but i messed up my math.

Answer 1

$\bold{\huge{\underline{ Solution }}}$

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

$\bold{\red{ = 2( lb + bh + hl)}}$

Subsitute the required values,

$\sf{ = 2[(7)(7) + (7)(12) +(7)(12) ]}$

$\sf{ = 2[ 49 + 84 ]}$

$\sf{ = 2[ 49 + 168 ]}$

$\sf{ = 2[ 217 ]}$

$\bold{ = 434 cm^{2}}$

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

$\sf{ = 2[(2)(7) + (7)(2) +(2)(2) ]}$

$\sf{ = 2[ 14 + 14 + 4 ]}$

$\sf{ = 2[ 28 + 4 ]}$

$\sf{ = 2[ 32]}$

$\bold{ = 64 cm^{2}}$

The common base area of both the cuboids

$\sf{ = lb }{\sf{ + lb}}$

$\sf{ = 14 + }{\sf{ 14}}$

$\bold{ = 28 cm^{2}}$

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,

$\sf{ = 434 + 64 - 28 }$

$\sf{ = 498 - 28 }$

$\bold{ = 470cm^{2}}$

Hence, The surface area of composite figure is 470 cm² .

Answer 2

Answer:

470cm²

Step-by-step explanation:

SA= (12*7)*4+(7*7)*2+(2*2)*2+(7*2)*2

=336+98+8+28

= 470 cm²

Therefore, the surface ares is 470 cm².

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