Question

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

Answer 1

470cm²

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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Answer 2

`\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 .