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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?

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 class=

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Answer:

The area of the metal part or shaded area is S=10x+45.

Step-by-step explanation:

The shaded area can be calculated substracting the little square area (the hole) from the big square area (the original metal part).

This is:

[tex]S=S_{original}-S_{hole}=(x+7)^2-(x-2)^2\\\\S=(x^2+14x+49)-(x^2-4x+4)\\\\S=(14-4)x+(49-4)\\\\S=10x+45[/tex]

The area of the metal part or shaded area is S=10x+45.

The area of the metal part, or the shaded region shown is 10x + 45.

calculation:

[tex]= (x+ 7)^2 - (x-2)^2\\\\= (x^2 + 14x + 49) - (x^2 - 4x + 4)\\\\= (14 - 4)x + (49 - 4)[/tex]

= 10x + 45

Learn more about the area here; https://brainly.com/question/17064026

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