Intro to Geometry in 2D

These are your notes for Area of 2 Dimensional figures…Write & Draw EVERY detail as if I was at the front of class. Write down any questions you may

have, ask the substitute, or a neighbor!

By:Jeffrey McAven

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COME ON! GET MOVING GUYS!

Lets look at 2 Dimensional Shapes and their Formulas

Triangles (3 sides) Quadrilaterals (4

sides) Polygons-3 or more sides, must be closed,

no curved or overlapping sides

Polygons-Any closed shape made up of straight lines.We have already talked about Triangles and Quadrilaterals, lets look at some more common polygons.

Pentagon (5 sides) Hexagon (6 sides) Heptagon (7 sides) Octagon (8 sides) Nonagon (9 sides) Decagon (10 sides)

You do not need to know the formulas for these but should be able to recognize them.

PerimeterTo find the perimeter of any polygon all you need to do is add the sides.

Perimeter

QuadrilateralsA Quadrilateral is any four sided figure. Lets look at the most common.

Square – All Sides and Angles sameA=s2 or A=base(height)

Rectangle – All Angles are the same and parallel sides are the same measure A=base(height)

Squares and Rectangles

s

sA = s²

6

6A = 6² = 36 sq. units

b

hA = bh

12

5

A = 12 x 5 = 60 sq. units

Example:Example:

Area of Rectangle: A = bhArea of Square: A = s²

QuadrilateralsParallelogram – Parallel side are the same A=bh

Rhombus A=bh

Trapezoid

h

bbA

221

Parallelograms & RhombusArea of Parallelogram: A = b(h)

6

9

A = 9 x 6 = 54 sq. units

h

b

Example:

Example:

Area of Rhombus: A = b(h)

The height (h) is the distance between the two bases b1 & b2, perpendicular to each base

Trapezoids

h

b1

b2

h

bbA

221

Or

TrianglesA Triangle is a three sided figure. All triangles have the same Area formula or2

bhA bhA

2

1

TrianglesRight Triangle – Has one angle 90○

Acute Triangle – Every angle is less than 90○

Obtuse Triangle –Has one angle more than 90○

TrianglesEquilateral Triangle – All angles and sides are the same measure

Isosceles Triangle – Two sides are the same and two angles are the same

Scalene Triangle – All sides and angles are different

Triangles1

2Area of Triangle A bh

h

h

b

b

h is the distance from a vertex of the triangle perpendicular to the opposite side.

Or

Circles Circumference of a circle is the distance around the outside of the circle. The formula is C=2πr or C= πd

Area formula for a circle is A= πr2

Area formula for a circle is A= πr2

Area of a Circle

Circumference of a CircleCircumference formula for a circle is

or

Area of Composite Figures

8

10

12

4 14

8

The area of a composite figure is the sum of all of its non-overlapping parts.

A = ½(8)(10)

A= 40

A = (12)(10)

A= 120

A = (4)(8)

A=32

A = (14)(8)

A=112

Area = 40 + 120 + 32 + 112 = 304 sq. units

Answers:1)140cm2

2)56cm2

3)180cm2

4)168cm2

5)132cm2

6)240cm2

7)330cm2

8)72cm2

9)72cm2

10)180cm2

11)140cm2

12)240cm2

13)225cm2

14cm

10cm

7cm

8cm

12cm

15cm

14cm

30cm

15cm11cm9cm

20cm

12cm

11cm

12cm

16cm

14cm

9cm

12cm

12cm

18cm

20cm

12cm

14cm

8cm25cm

12cm15cm

14cm

16cm

15cm

12 3

4

5 67

89

10

11

1213

12cm

12cm

8cm

4cm

13cm

15cm

9cm

9cm

40cm

15cm

11cm

9cm

12cm

12cm

14cm

12cm

18cm

14cm20c

m

8cm

8cm

8cm

40cm

22cm

14cm

18cm 35c

m 12cm

25cm

24cm

36cm

15cm

12 3

4

5 67

89

10

11

12 1

3

15cm

Try these

onyour

own!!!