Shaded Area

Area of odd figures caused by inscribed shapes

by Lloyd Thomas

​Because of time constraints, this will be your only area from inscribed shapes practice. It will appear on your quiz, scheduled for Friday (B-day) or Monday (A-day)

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All problems in this lesson are for a grade on correctness. This is to ensure attentiveness and participation.​

​Our next step in exponent rules is finding areas of odd shapes caused by inscribed figures (figures that are within another figure)

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​An easy entry way is figures without variables and exponents - just numbers.

​We have a big rectangle and a little rectangle. If we are asked to find the area of the shaded region, then how much of the area of the big rectangle is missing?

Yes, the big rectangle is missing an amount of area equal to the little rectangle.

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So, what can we do to find the shaded area using these two figures?

Yes, Find the area of the big rectangle and the area of the small rectangle and subtract the two figures.

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This would give you the area of the shaded part.

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Now go do it! Put your work on your Notes page.

​(You'll get 30 seconds)

Multiple Choice

What is the area of the shaded region?

• 14 m²
• 120 m²
• 106 m²
• 134 m²

​So, here is the work you should have done

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​Find the area of the big figure and find the area of the smaller figure, then subtract the two

​That's it! That's the basics. You are taking the area of the figure inside and subtracting it from the area of the figure that's on the "outside" Now you try! (1 min)

Multiple Choice

Find the area of the shaded region.

• $$99\ ft^2$$

• $$114\ ft^2$$

• $$69\ ft^2$$

• $$54\ ft^2$$

​If you got the question wrong, then here is what you should have done. Copy it down if you need (but quickly)

​Try another one (2 minute)

Multiple Choice

Solve. Use 3.14 for pi. Give your answer in cm^2.

• 386.97 cm²
• 122.46 cm²

• 50.24 cm²

• 102.42 cm²

​If you got the question wrong, then here is what you should have done. Copy it down if you need (but quickly)

​Nothing changes if you are working with monomials with variables. You've learned how to add, subtract, multiply and divide monomials with variables, solving these kinds of problems using them shouldn't be a big adjustment.

​Find the area of the shaded region

​What are the outer and inner shapes?

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​Write down their area formulas and identify the numbers you will plug in to the equations

​What you should have determined

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​Now do the work and find the area

of the shaded region

​Your work...

​Square Area Circle Area

​That's about it. If you need additional practice then see me during advisory. I can't spend any more class time on this. This will be on your scheduled Quiz on Friday (10/29 B-day) or Monday (11/1 A-day)

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​On to Simplifying Radicals