Area of Plane, Reg, & Composite Figures, Shaded Regions, Sector

Area of Plane Figures

We can think of the area of a two-dimensional ("plane") object as the number of square units it contains.

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Each of the figures to the right has the same area.

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You can see that counting boxes sometimes works well and sometimes not.​

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Fortunately, there are formulas so we don't have to count boxes

Rectangle formula is pretty straightforward

In middle school you probably learned "length times width" but because the formulas of many shapes are related we want to develop some common language. So we will say the area of a rectangle is "base times height".

Some text here about the topic of discussion

​On the next slide we'll look at the relationship between area of a rectangle and area of a triangle.

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Open Ended

Explain why the area of a triangle is half the area of a rectangle with the same base and height.

Open Ended

Determine the area of the triangle

A reminder

​Recall from Unit 6 (properties of polygons)

Multiple Choice

Determine the area of the parallelogram:

• 166.41 sq. in

• 91.59 sq. in.

• 45.8 sq. in.

• 1181.51 sq. in.

The trapezoid area formula has a slight twist. It is half the height times the sum of the two bases.

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Open Ended

Determine the area of the trapezoid:

Multiple Choice

How would you calculate the area of this circle?

• $$A=\left(26\right)^2\cdot\pi$$  

• $$A=\left(3.14\right)\left(13\right)$$  

• $$A=26\pi$$  

• $$A=\left(13\right)^2\cdot\pi$$  

Open Ended

What is the area of the circle?

Area of Regular Polygons and Composite figures

Draw

Study for next few problems

Multiple Choice

Find the area of the composite figure. Round your answer to the nearest tenth.

• 122.1 m²

• 128.1 m²

• 134.1 m²

• 138.1 m²

Multiple Choice

Find the area of the shaded figure.

• 6 cm²

• 36 cm²

• 42 cm²

• 48 cm²

Multiple Choice

Find the area of the composite figure.

• 156 cm²

• 166 cm²

• 176 cm²

• 186 cm²

Multiple Choice

Find the area of the regular hexagon. Round your answer to the nearest tenth.

• 49.4 ft²

• 51.4 ft²

• 53.4 ft²

• 55.4 ft²

Area Of Regular Polygons

​Objective: Find the areas of regular polygons

Multiple Choice

REGULAR in Maths means...

• Normal

• Two sides have the same length

• All sides are equal and all angles are equal

• It has right angles

Multiple Select

Which of these figures are regular polygons?

Multiple Choice

In a regular polygon, the line from the center to an outer vertice is a(n)

• Apothem

• Central Angle

• Radius

• Regular Polygon

Multiple Choice

In a regular polygon, the line drawn from the center of a polygon to a midpoint on one side is called

• Apothem

• Central Angle

• Radius

• Regular Polygon

Quick Review!

Check out out formula before you practice!

Multiple Choice

What is the formula for area of a regular polygon.

• ½⋅apothem⋅perimeter

• a² + b² = c²

• πr²

• √x²+y²

Draw

Find the Area. Height = 12

Multiple Choice

Find the area of this composite figure

• 6 cm²

• 7 cm²

• 8 cm²

• 9 cm²

Multiple Choice

Find the area of a regular hexagon with a side length of 9 cm.

• 210.4 cm²

• 230.1 cm²

• 237.0 cm²

• 260 cm²

Area of

Irregular polygons

(Missing/Shaded Regions)

_{I can decompose irregular polygons into quadrilaterals and triangles to find their area.}

​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)

​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

Area of Circles and Sectors and Segments

Area of Circles

Multiple Choice

What is the area of this circle?

• 82.13 m²

• 78.50 m²

• 314.16 m²

• 170.12 m²

Multiple Choice

Madalyn's dining room table is round and has a radius of 4.5 feet. What is the tabletop's area?

• 63.585 ft²

• 68.345 ft²

• 64.585 ft²

• 61.345 ft²

Area of a sector

Multiple Choice

Find the area of the sector outlined in bold.

• 52.4 in²

• 18,864 in²

• 60 in²

• 10.47 in

Multiple Choice

A cathedral window is built in the shape of a semicircle. If the window is to contain three stained glass sections of equal size, what is the area of each stained glass section?  Express answer to the nearest square foot.

• 1 sq. ft

• 13 sq. ft

• 3 sq. ft

• 26 sq. ft

Multiple Choice

Find the area of the shaded sector of circle O.  The radius is 6 inches and the central angle is 100°.  Express answer to the nearest tenth of a square inch.

• 9.2 sq. in.

• 10.5 sq. in.

• 31.4 sq. in.

• 38.2 sq. in.

Multiple Choice

What is the formula for finding the area of a sector. 

• $$\left(\frac{n}{360}\right)\pi r^2$$

• $$2\pi r$$

• $$\pi r^2$$

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Multiple Choice

What is the name of the blue region?

• A sector

• A segment

• A hooly bob

• A central angle

Fill in the Blanks

Multiple Choice

What is the area of the shaded segment?

• 185.0619

• 88.9359

• 39.3078

• 5.7975

Multiple Choice

What is the area of this circle?

• 4π

• 8π

• 16π

• π

Multiple Choice

Find the area of the shaded sector?

• 14 cm squared

• 139.6 cm squared

• 27.9 cm squared

• 558.5 ft squared

Multiple Select

What is/are the formula(s) to find the area of a circle?

• πr²

• 2πr

• √π

Multiple Choice

What is the area of the shaded segment? Leave your answer as an exact value.

• 25π - 50

• 25π - 100

• 5π - 50

• 5π - 100

Multiple Choice

what is the area of this semicircle ?

• 100.48cm²

• 80cm²

• 200.96cm²

• 25.12cm²

Multiple Select

is the formula for?

• arc length

• area of a sector

• area of a segment

• arc measure

Multiple Choice

Strategy to find the area of the shaded purple segment...

• get the area of the circle and subtract out the sector

• get the area of the sector and subtract out the triangle

• get the area of the triangle and subtract the segment

• press skip and simply move on...