1. Perimeter, Circumference, and Area
Sec. 1-9
Perimeter, Circumference, and Area
Objective: Find the perimeters and areas of rectangles, squares, & the circumferences of circles.

2. Definitions Perimeter – Distance around a figure
Sum of the lengths of its sides.
Units are regular
cm, in, ft
Area – Is the number of square units a figure encloses.
Units are squared
cm2, in2, ft2

3. A = l x w A = b x h Square * 4 right angles
* All 4 sides are congruent ()
Perimeter = sum of all 4 sides
Ps = s + s + s + s
Ps = 4s
A = l x w
A = b x h

4. Example: 1
A square has side with a length of 5cm. What is the perimeter and area of this square.
*Draw and label a diagram first!!
5cm
Ps = 4s
Ps = 4(5cm)
Ps = 20cm
As = l x w
As = 5cm x 5cm
As = 25cm2

5. Example 2
The area of a square is 81cm2. How long is each of its sides.
81cm2
As = l x w
As = s x s
As = s2
81cm2 = s2
√81cm2 = √s2
9cm = s

6. Rectangles Two pairs of congruent sides. length
Opposite sides are congruent
4 right angles
PR = 2l + 2w
A R = l x w
length
w w

7. Example 3: Rectangle
Example 3: Find the perimeter and area of the following rectangle. 9m
12m
PR = 2l + 2w
PR = 2(12m) + 2(9m)
PR = 24m + 18m
PR =42m
AR = l x w
AR = 12m x 9m
AR = 108m2

8. Quadrilateral ABCD has vertices
A(0, 0), B(9, 12), C(11, 12), and D(2, 0).
Find the perimeter.
Draw and label ABCD on a coordinate plane.
Find the length of each side. Add the lengths to find the perimeter.
AB = (9 – 0)2 + (12 – 0)2 = Use the Distance Formula.
= = = 15
BC = |11 – 9| = |2| = 2 Ruler Postulate
CD = (2 – 11)2 + (0 – 12)2 = (–9)2 + (–12)2Use the Distance Formula.
= = = 15
1-7
DA = |2 – 0| = |2| = 2 Ruler Postulate

9. Perimeter = AB + BC + CD + DA
(continued)
Perimeter = AB + BC + CD + DA =
= 34
The perimeter of quadrilateral ABCD is 34 units.
1-7

10. Circles
Circle – A set of points equal distance from a given point.
* The given point is called the
CENTER
Radius- segment with endpoints at the center of the circle and on the circle.
Diameter – Segment in a circle with endpoints on the circle and contains the center of the circle. r d
2r = d

11. Circles continued
Circumference – Distance around the circle * The perimeter of the circle.
C = d or C = 2r
Area of a circle
* How many square units inside the circle.
* Units squared
AC = r2

12. Example 4 3
Find the circumference and the area of a circle with a radius of 3ft.
C = 2r
C = 2(3ft)
C = 6ft
C = 18.8ft
AC = r2
AC = (3ft)2
AC = 9ft2
AC = 28.3ft2

13. Example 5 & 6
The diameter of a circle is 16mm. Find its Circumference.
C = 2r
C = 2(8mm)
C = 16mm
C = 50.3mm
The circumference of a circle is 28in. What is its radius?
C = 2r
28in = 2r
2 
r = 4.5in

14. Draw a horizontal line to separate the figure into three
Find the area of the figure below.
Draw a horizontal line to separate the figure into three
nonoverlapping figures: a rectangle and two squares.
1-9

15. Find each area. Then add the areas.
(continued)
AR = bh Formula for area of a rectangle
AR = (15)(5) Substitute 15 for b and 5 for h.
AR = 75
AS = s2 Formula for area of a square
AS = (5)2 Substitute 5 for s.
AS = 25
A = Add the areas.
A = 125
The area of the figure is 125 ft2. -9

16. 2 Postulates
P(1-9) If 2 figures are congruent, then their areas are equal.
II. P(1-10) The area of a region is the sum of the area of its nonoverlapping parts.

17. Example 7: Composite Figure
Find the perimeter and area of the following figure.
P = 16cm + 16cm + 8cm + 3cm + 3cm + 2cm
P = 48cm

18. Example 7 continues: Area of composite figure
A1 = l x w
A1 = 8cm x 7cm
A1 = 56cm2
A2 = l x w
A2 = 5cm x 4cm
A2 = 20cm2
A3 = l x w
A3 = 2cm x 5cm
A3 = 10cm2
AT = A1 + A2 +A3
AT = 56cm2 + 20cm2 +10cm2
AT = 86cm2

19. Ex.8: Find the Area of the following figure.
Ab = l x w
= 50in x 30in
=150in2
As = l x w
= 10in x 5in
=50in2
At = Ab – As
= 100in2