Name: ____________________________________________________ Date: _________________ Block: ___________
Chapter 11: Area and Perimeter
Shape
Perimeter/Circumference Formula
Area Formula
Square
Rectangle
Triangle
Circle
Parallelogram
Trapezoid
Rhombus
Kite
Remember1) You might need to break the figure into different figures to calculate the entire area.
2) You might need to use Pythagorean Theorem to find missing lengths.
EX 1: Find the perimeter or circumference of the following shapes. Then find the area of the shape.
A)
B)
C)
Perimeter = ______
Perimeter = ______
Perimeter = ______
Area = ______
Area = ______
Area = ______
D)
E)
F)
Perimeter= _________
Perimeter= _________
Circumference= _________
Area=___________
Area=___________
Area=___________
I---------12------------I
EX 1: Find the perimeter of the following shapes. Then find the area of the shape.
A)
B)
C)
EX 2: Find the area of the shaded figures.
A)
B)
EX 3: Use the given information to find the value of the indicated measure or the value of x.
a) Find the DIAMETER of the circle:
b) Find the radius of a circle with a circumference of 52 ft.
Classify Polygons
Polygons are named for the number of sides that they have.
Ex. 2: Identify the type of polygon and state whether the polygon is convex or
# of Sides Type of polygon
concave.
3
4
a)
b)
5
6
7
8
9
10
c) Draw a convex pentagon.
d) Draw a concave hexagon
n
Angles in Polygons
Polygon Interior Angles Theorem
Formula for SUM: to find the sum of
the interior angles of any convex
polygon
Formula for each Interior angle: to
find a single angle find the sum and
divide by number of sides
Sum of Interior  = ( n  2)  180
One Interior  =
2
(n  2)  180
n
where n  number of sides
where n  number of sides
Ex. 1: Find the sum of the measures of the interior angles of the convex polygon. Then find the measure of EACH
interior angle.
A. 16-gon
B. 23-gon
Sum: ____________________
Sum: _____________________
Interior Angle: ____________
Interior Angle: _____________
Ex. 2:
Find the value of x in the diagrams below.
A.
B.
Triangle
Quadrilateral
C.
Pentagon
Hexagon
Heptagon
Octagon
n-gon
Name
# of Sides
Sum of
Interior
Interior
Angle
Ex. 3: The measure of each interior angle of a regular polygon is given below. How many sides does each
polygon have?
A. 140
B. 165
Polygon Exterior Angle Theorem
Formula for Sum
Formula for each exterior angle
Ex. 5:
Ex. 6:
The Sum of Exterior Angles = 360
One Exterior Angle =
Find the value of x in each diagram.
A.
360
where n  number of sides
n
B.
Given the measure of each exterior angle of a regular n-gon, find the value of n.
A. 40
B. 30
3
Circumference and Arc Length
Circumference
C  2  r
Formula:
EX 1: Find the circumference of the circle:
a) r=6
b) r=10
c) d=15
d) d=9
ARC LENGTH Formula:
ArcLength ArcMeasure

2  r
360
EX 2: Find the lengths of each arc:
A)
B)
C)
EX 3: Use the ARC LENGTH to find the indicated measure:
A) Find the circumference of the circle:
B) Find the radius of the circle:
Areas of Circles and Sectors
Area Formula:
A  r
2
EX 1: Find the Area of the circle:
a) r=6
b) r=10
c) d=15
SECTOR OF A CIRCLE: FORMULA
AreaSector ArcMeasure

360
 r2
EX 2: Find the area of the sector for each
A)
B)
4
d) d=9