Question

The sum of length,breadth and depth of a cuboid is 21cm and the length of its diagonal is 13cm.find the surface area of the cuboid.​

Answer 1

The surface area of the cuboid is 272 cm²

Step-by-step explanation:

Let,

Length = l

Breadth = b

Height = h

The sum of length,breadth and depth of a cuboid is 21cm

So,

⇒ l + b + h = 21 cm

★ Diagonal of cuboid = 13 cm

$\sqrt{ {l}^{2} \: + \: {b}^{2} \: + \: {h}^{2} } \: = \: {13}^{2}$

$\sqrt{ {l}^{2} \: + \: {b}^{2} \: + \: {h}^{2} } = {13}^{2} = 169$

${(l \: + \: b \: + \: h)}^{2} \: = \: {21}^{2}$

${(l \: + \: b \: + \: h)}^{2} = ( {21})^{2} = 441$

${l}^{2}+{b}^{2}+{h}^{2}+2(lb+bh+lh)=441$

⇒ 169 +  total surface area = 441

⇒Find  TSA of cuboid:

⇒ TSA

⇒ 441 - 169

⇒ 272 

Therefore,

The surface area of the cuboid is 272 cm²

Answer 2

Let , the length , breadth and height of triangle be " L " , " B " and " H "

First Condition :

The length of its diagonal is 13 cm

We know that , the diagonal of cuboid is given by

D = √(L)² + (B)² + (H)²

Thus ,

13 = √(L)² + (B)² + (H)²

Squaring on both sides , we get

169 = (L)² + (B)² + (H)²

Second Condition :

The sum of length,breadth and depth of a cuboid is 21 cm

L + B + H = 21

Squaring on both sides , we get

(L + B + H)² = 441

(L)² + (B)² + (H)² + 2(LB + BH + HL) = 441

169 + CSA of cuboid = 441

CSA of cuboid = 272 cm²

$\sf \therefore \underline{The \: CSA \: of \: cuboid \: is \: 272 \: {cm}^{2} }$

Remmember :

CSA of cuboid = 2(LB + BH + HL)