Transcript Lesson 1 Contents

Lesson 11-1
Areas of Parallelograms
Objectives
• Find perimeters and areas of parallelograms
– P = 2 (l + w)
– A = b·h
• Determine whether points on a coordinate
plane define a parallelogram
Vocabulary
• base – the “horizontal” distance of the parallelogram
(bottom side)
• height – the “vertical” distance of the parallelogram
• area – the amount of flat space defined by the figure
(measured in square units)
• perimeter – once around the figure
Area of Parallelograms
A
B
Parallelogram Perimeter
Add length of all four sides
P = AB + DB + DC + CA
(or P = 2AB + 2BD)
C
A
B
Parallelogram Area
b
A=h·b
h is height
b is base (AB or CD)
(similar to a rectangle)
h
C
D
D
Example 1:
A
Find the perimeter and area of
parallelogram ABCD
B
15
12
C
P = 2(12 + 15) = 2(27) = 54
A = bh = 15(10) = 150 square units
10
D
Example 2:
M
Find the perimeter and area of
parallelogram MNOP
N
15
10
P = 2(10 + 15) = 2(25) = 50
P
6
9
A = bh = 15(h) = 15h square units
10² = 6² + h²
100 – 36 = 64 = h²
√64 = 8 = h
So, area = 15(8) = 120 square units
O
Find the perimeter and area of
.
Base and Side: Each pair of
opposite sides of a parallelogram
has the same measure. Each base
is 32 inches long, and each side is
24 inches long.
Perimeter: The perimeter of a polygon is the sum of the
measures of its sides. So, the perimeter of RSTU is
2(32) + 2(24) = 112 inches.
Height:
Use a 30-60-90 triangle to find the height. Recall that
if the measure of the leg opposite the 30 angle is x,
then the length of the hypotenuse is 2x, and the length
of the leg opposite the 60 angle is x√3 .
24 = 2x
Substitute 24 for the hypotenuse.
12 = x
Divide each side by 2.
So, the height of the parallelogram is x√3 or
12 √3 inches.
Area:
Answer:
The perimeter of
RSTU is 112 inches, and the
area is about 665.1 square inches.
Example 3:
D
Find the perimeter and area of
parallelogram DEFG
E
27
21
h
P = 2(21 + 27) = 2(48) = 96
60°
G
F
A = bh = 27(h) = 27h square units
(side opposite 60°) h = ½ hyp √3
h = ½ (21) √3
h = 10.5 √3
So, area = 27(10.5√3) ≈ 491 square units
The Kanes are planning to sod some parts of their yard. Find the
number of square yards of grass needed.
To find the number of square
yards of grass needed, find
the number of square yards of
the entire lawn and subtract
the number of square yards
where grass will not be
needed. Grass will not be
needed for the vegetable
garden, the garage, or the
house and walkways.
Entire lawn:
Vegetable Garden:
Garage:
House and Walkways:
Area
Entire Lawn
Vegetable
Garden
Garage
House and
Walkways
The total area is 30,000 – 2000 – 3000 – 6000 or 19,000 square feet.
There are 9 square feet in one square yard, so divide by 9 to
convert from square feet to square yards.
Answer:
They will need about 2111 square yards of sod.
The Wagners are planning to put hardwood floors in their dining
room, living room, and kitchen. Find the number of square yards of
wood needed.
Answer:
Summary & Homework
• Summary:
– The area of a parallelogram is the product of the
base and the height
• Homework:
– pg 598-600; 9-16, 27, 28