M 1312
1
8.1 & 8.2
Square units are used to measure area.
AREA formulas for REGULAR polygons:
parallelogram
=
bh
b
l = length
w = width
P = perimeter
b = base
h = height
d = diagonal
r = radius
m = median
a = apothem (you may need to use trig. to find this)
h
rectangle/square =
lw
l
l
w
w
triangle
1
bh
2
=
h
b
Example 1:
What is the total area of the figure below:
6
18
18
6
In this example we used the Postulate 20 (Area Addition Postulate)
Let R and S be two enclosed regions that do not over lap.
A R S  A S  A R
M 1312
2
8.1 & 8.2
Example 2: Find the area of the parallelogram.
80 cm
60 cm
50 cm
Example 3: Find the area of the given
figure.
12 in
3 in
6 in
8 in
Example 4:
Find the height of the triangle. Area = 56
h
14
Example 5: Find the area of the entire figure (a rectangle and a triangle).
20
10
6
M 1312
3
8.1 & 8.2
Example 6:
Find the area of an equilateral triangle. Each side is 16.
You will need to find the height first.
Example 7: Find the area of the shaded region.
A.
11
4
5
4
B.
12
3
4
15
8
7
7
C.
9.2
9.2
3.1
10.8
3.1
M 1312
4
8.1 & 8.2
Perimeter of a Triangle:
a
b
P = a + b +c
P=a+a+b
a
a
c
b
Scalene
Isosceles
a
a
P = a+ a+ a
a
Equilateral
Perimeter is always the sum of the length of the sides.
1
Area of trapezoid= (h)(b1 + b2) OR
2
A = mh
b1
h
h
m
b2
Area Kite or rhombus =
1
(d )(d2)
2 1
( this formula works for any
quadrilateral with perpendicular
diagonals)
d1
d2
M 1312
5
8.1 & 8.2
Section 8.2
8.2.1: Heron’s Formula: For any triangle with sides of lengths a , b and c , the area is found
by
 where s is the semiperimeter of ABC
8.2.2:Brahmagupta’s Formula: For a quadrilateral with sides a , b , c , and d the area is
Where
8.2.7: The ratio of the areas of two similar triangles (or any similar polygons) equals
the squares of the ratios of the lengths of any two corresponding sides.
Example 1: Find the area
19
26
Example 2:
What is the total perimeter of the figure below:
6
18
18
6
M 1312
6
8.1 & 8.2
Example 3: Find the perimeter of the shaded region.
5
4
5
5
5
4
4
5
5
5
4
5
Example 4: From the given information, find the length of the altitude.
A = 95
8
x
11
Example 5:
A trapezoid has an area of 75 square inches, the height is 6 inches and one of
the bases is 8 inches. Find the other base of the trapezoid.
Example 6: These figures are both a rhombus.
a.
A = __________
10
12
12
10
M 1312
7
8.1 & 8.2
b. A = _____________
10
12
Example 7: Given a rhombus, find the value of x
A = 56
8
x
8
Example 8:
A rhombus has a perimeter of 100 meters and a diagonal 30 meters long. Find
the area of the rhombus. Hint: you must find the other diagonal.
M 1312
8
Example 9:
8.1 & 8.2
The height of a trapezoid is 9 cm. The bases are 8 cm and 12 cm long. Find the
area.
Example 10:
The area of a trapezoid is 80 square-units. If its height is 8 units, find the
length of its median.
Math 1312 Popper 21: Popper 21 question 1: Find x:
x 90 140 91 A. 29 B. 55.5 C. 26 D. None of these Popper 21 question 2: Solve for x:
x 165 A. 170 B. 86.5 C. 97.5 D. None of these Popper 21 question 3: Find the m DEC given arc DC = 30, arc AB = 80.
A. 80
B. 30
C. 55
D. 45 
E. None of these
Popper 21 question 4: Find the value of “x” in the circle below.
30 40 x A. 40 B. 60 C. 100 D. None of these Popper 21 question 5:
Find the AE given DE = 5, BE = 12 and CE = 8.
A. 19.6
B. 7.5
C. 13.6
D. 12
E None of these
Math 1312 Popper 22 Popper 22 question 1 : For each figure, find the value of x. A. B. C. D. None of these Math 1312 Popper 22 Popper 22 question 2 : For each figure, find the value of x. A. 2 B. C. 25 D. None of these Popper 22 question 3: For each figure, find the value of x. A. 6 B. 3√13 C. 36 D. None of these Popper 22 question 4: Find the exact value of “x”. 60° x 30° 9 A. 6 B. 9√3 C. 3√3 D. None of these Popper 22 question 5: Find the exact value of “x”. 45 3 x A. 45 √2 B. 3√2 C. 6 D. None of these