3.3b: Area and Perimeter M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures (including composite figures)

3.3b: Area and Perimeter

M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures (including composite figures) or surface area or volume of three

- Quadrilaterals and composite shapes

G-GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

G-GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.?

CCSS:

GSE’s

Area of Parallelograms

Base (b) = One side of the parallelogram

Height (h) = distance between the bases (must be perpendicular)

Base

Base

height

Area of a Parallelogram = (b)(h)

Why ?

Base

Base

height

What shape will it make when we cut off the triangle on the side and put in on the other side?

A rectangle with the area= (base)*(height)

How many square yards of carpeting are needed to cover the family room, hallway, and bedroom?

Area if Triangles

bhA2

1

*b= base of the triangle

*h = height of the triangle

* Both are touching the 90 degree angle in the triangle

But Why ?

b

h h

It is half of a parallelogram with the same exact base and height

Area if a Rhombus

Area = 212

1dd

diagonal one 1 d

diagonal second the2 d

1d

2d

Example

A rhombus has an area of 50 square mm. If one diagonal has a length of 10 mm,How long is the other diagonal.

Area of a Trapezoid

)(2

121 bbhA

bases) ebetween th distance (the heighth Base (parallel side)

Base

Height (has to be perpendicular to bases)

side parallel (opposite baseother theb

side) parallel (a bases theof one

2)

1

b

Example

#1- Find the area #2 - Find the area

M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope.

Find the area

Use a geometric (area) approach Instead of algebraic (slope, distance)

Now you have a rectangle With dimensions of 4 by 6.

2

rectangle units 24)6)(4( Area4 units

6 units

To get the area of the original triangle, subtract the new triangles from the overall rectangle. This will leave you with the area of the original triangle.

1

23

2

3

2

2

2

1

u 4)4)(2(2

1

u 6)6)(2(2

1

u 4)4)(2(2

1

A

A

A

2

s trianglerectangleTriangle Original

u 10

14 - 24

smallerAAA

Now you try an example

Does it work with other shapes?

The end

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