10.1 - Area of Plane Figures

10.1 - Area of Plane Figures

By Steve Dull

Objective

​To find area of parallelograms, triangles, trapezoids, and circles.

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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​https://www.geogebra.org/m/jmgu5t2z

Open Ended

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

Let's Practice

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?

Independent practice

Some text here about the topic of discussion