If the sum of length, breadth and height of a cuboid be 19 cm and the length of its diagonal be 11 cm, then· what will be the total surface area of the cuboid ?

Explanation

Let the length, breadth and height of the cuboid be a cm, b cm and c cm respectively.
As per question `a+b+c= 19` and ` sqrt( a^2 + b^2+c^2)=22 ` or, `a^2+b^2+c^2=121`
Now, `(a+b+c)^2 =19^2 =361 `
`rArr a^2+b^2+c^2+2 (ab+bc+ca) = 361`
`121 + 2(ab+bc+ca)= 361 [ :' a^2+b^2+c^2= 121]`
`rArr 2(ab + bc+ca) = 381 -121 = 240`.
Hence the required total surface area of the cuboid is 240 sq-cm.