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?

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,

Substituting s = x + 7, we get;

Thus, the area of the metal is square units.

Area of the hole:

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

Substituting s = x -2 ,we get;

Thus, the area of the hole is 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;

Simplifying, we have;

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

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step-by-step explanation: