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! 
HAVE YOU NOT
GOT OFF THIS
SLIDE YET?
COME ON! GET
MOVING GUYS!
 By:Jeffrey McAven
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.
Perimeter
 To find the perimeter of any polygon all you need to do is add the
sides.
Perimeter
Quadrilaterals
A Quadrilateral is any four sided figure. Lets look at the most
common.
 Square – All Sides and Angles same A=s2 or A=base(height)
 Rectangle – All Angles are the same and parallel sides are the
same measure
A=base(height)
Squares and Rectangles
Area of Square: A = s²
A = s²
Example:
6
A = bh
s
h
b
Example:
s
6
Area of Rectangle: A = bh
5
A = 6² = 36
sq. units
12
A = 12 x 5 = 60 sq. units
Quadrilaterals
 Parallelogram – Parallel side are the same
A=bh
 Rhombus
A=bh
 Trapezoid
A
b1  b2  h
2
Parallelograms & Rhombus
Area of Parallelogram: A = b(h)
Area of Rhombus: A = b(h)
Example:
h
b
Example:
6
9
A = 9 x 6 = 54 sq. units
Trapezoids
1
Area of Trapezoid A = h(b1 + b2 )
2
Or

b1  b2 
A
h
2
The height (h) is the distance between the two bases b1 & b2,
perpendicular to each base
b2
h
b1
Triangles
A Triangle is a three sided figure. All triangles have the same
bh
Area formula
or
1
A
2
A
2
bh
Triangles
 Right Triangle – Has one angle 90○
 Acute Triangle – Every angle is less than 90○
 Obtuse Triangle –Has one angle more than 90○
Triangles
 Equilateral 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
Triangles
1
Area of Triangle A  bh Or
2
A=
bh
2
h is the distance from a vertex of the
triangle perpendicular to the opposite side.
h
b
h
b
Pi = P
Circles
P
@
3.14
 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
Pi = P
Area of a Circle
 Area formula for a circle is A=
πr2
P @ 3.14
Circumference of a Circle
 Circumference formula for a circle is
C=P(Diameter)
or
C = 2P(radius)
P @ 3.14
Area of Composite Figures
The area of a composite figure is the sum of all of its nonoverlapping parts.
8
10
4
8
14
12
A = ½(8)(10)
A = (12)(10)
A = (4)(8)
A = (14)(8)
A= 40
A= 120
A=32
A=112
Area = 40 + 120 + 32 + 112 = 304 sq. units
3
2
1 14cm
15cm
8cm
4
10cm
12cm
7cm
6
9cm
5
12cm
14cm
7
12cm
11cm
15cm
12cm
11cm
30cm
20cm
8
14cm
9
12cm
10
18cm
9cm
16cm
11
8cm
12cm
12cm
20cm
12
13
25cm
14cm
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
15cm
12cm
14cm
15cm
16cm
3
2
1
12cm
9cm
13cm
8cm
4
15cm
4cm
15cm
6
9cm
5
9cm
12cm
11cm
12cm
14cm
14cm
9
8cm
10
8cm
20cm
18cm
11
18cm
14cm
22cm
15cm
40cm
12cm
8
Try
these
on
your
own!!!
7
8cm
40cm
12
35cm
12cm
25cm
13
24cm
15cm
36cm