Question

a rectangular wall with a length of 10x and width of 20 x has a rectangular doorway with a length of 5x and a width of 2x. What is the surface area of the wall?

Answer 1

∴ The the surface area of the wall is
`190x^(2) \ square\ unit`.

Explanation:

Given that,

The length of rectangular wall is
`10x`.

The width of rectangular wall is
`20x.`

The length of doorway is
`5x.`

The width of doorway is
`2x.`

and, we have to find the surface area of rectangular wall.

Now,

The length of rectangular wall is
`10x`.

The width of rectangular wall is
`20x.`

∴ Total surface area of a rectangular wall
`= Length\ of\ wall* Width\ of\ wall`

`= 10x* 20x`

`=`
`200x^(2) \ square\ unit`

Total surface area of a rectangular wall is
`200x^(2) \ square\ unit`.

Again, The length of doorway is
`5x.`

The width of doorway is
`2x.`

∴Total surface area of doorway
`=Lenght\ of\ doorway* Width\ of\ doorway`

`=5x* 2x`

`=10x^(2) \ square\ unit`

Total surface area of doorway is
`10x^(2) \ square\ unit`.

∴The remaining surface area of a rectangular wall is
`=`
`200x^(2) -10x^(2)`

`=190x^(2) \ square\ unit`

∴ The the surface area of the wall is
`190x^(2) \ square\ unit`.