Question

A hole is punched in a piece of metal to make a part for a machine.

What is the area of the metal part, or the shaded region shown?

Answer 1

Given:

The length of the side of the metal is x + 7.

The length of the side of the hole is x - 2.

We need to determine the area of the metal part or the shaded region.

Area of the metal:

The area of the metal can be determined using the formula,

`A=s^2`

Substituting s = x + 7, we get;

`A=(x+7)^2`

`A=x^2+14x+49`

Thus, the area of the metal is
`x^2+14x+49` square units.

Area of the hole:

The area of the hole can be determined using the formula,

`A=s^2`

Substituting s = x -2 ,we get;

`A=(x-2)^2`

`A=x^2-4x+4`

Thus, the area of the hole is
`x^2-4x+4` square units.

Area of the shaded region:

The area of the shaded region can be determined by subtracting the area of the hole from the area of the metal.

Thus, we have;

Area = Area of the metal - Area of the hole

Substituting the values, we have;

`Area = x^2+14x+49-(x^2-4x+4)`

Simplifying, we have;

`Area = x^2+14x+49-x^2+4x-4`

`Area = 18x+45`

Thus, the area of the shaded region is (18x + 45) square units.