Area of a Parallelogram
Area = product of its base and height
A= bh Base must be perpendicular to the height
b
h
5cm 3cm
9cm
A = 9(3)
A = 27
Example
Find the perimeter of a parallelogram, in which the base is 4ft and the area is 12 .
Need to find height
A = bh
12 = 4h
h = 3 ft
P = 2b + 2h
P = 2(6) + 2(3)
P = 18 ft
Area of a Triangle
Area = one half of the product of its base and height
A= bh or A = Base perpendicular to height
h h h
b b b
If b = 4” and h = 6”
Then A = (4)(6)
A = (24)
A = 12
Example—finding a side
The area of a triangle is 24 and its height is 3 cm. Find the length of its corresponding base.
A = for a triangle
24=
48 = 3b
b = 16 cm
Area of a Trapezoid
Area = (average of the bases)(height)
A = h
h
Remember: height is perpendicular to both bases
Example 1--Trapezoid
Find the area of the trapezoid. 20 in
25 in
18 in
36 in
A = h
A = 18
A = 18
A = 28(18)
A = 504
Example 2--Trapezoid
Find the area of the trapezoid. 11 ft
13 ft
16 ft
A = h find the missing height Find the hypotenuse
Use Pythagorean theorem
when solved you get …… h = 12 ft
A = 12
A =( ) 12
A = 27(6)
A = 162
Area of a Rhombus
The area of a rhombus is half the product of the lengths of its diagonals.
A =
Example: Find the area if the diagonals are: 6 in and 8 in
A =
A =
A =
A = 24
Area of a Kite
The area of a kite is half the product of the lengths of its diagonals.
A =
Example 1: Kite with diagonals 9 cm & 8 cm
A =
A =
A =
A = 36
Example 2--Kite
Find the area of the kite. 5” 4”
A = 6”
Find diagonalsWatch for right triangles = + so x = 3”
One diagonal is 2(4) = 8 inches Other diagonal = 3 + 6 = 9 inchesA = A = A = 36
Formulas
Square: A = bh
Rectangle: A = bh
Parallelogram: A = bh
Trapezoid: A = h
Triangle: A = ½ bh
Rhombus: A =
Kite: A =
Area Addition Postulate
The area of a region is equal to the sum of the areas of its nonoverlapping parts.
Best way to find this area is to find the
area of rectangle + area of triangle