Transcript Lesson 1 Contents - Headlee's Math Mansion

5-Minute Check on Lesson 11-1
Transparency 11-2
Find the area and the perimeter of each parallelogram. Round to the
nearest tenth if necessary.
17 ft
11 cm
1.
2.
13 cm
A = 204 ft²
A = 101.1 cm²
12 ft
P = 58 ft
P
=
48
cm
45°
3.
4.
A = 39.7 m²
P = 25.2 m
A = 171.5 in²
P = 58 in
11 in
60°
18 in
6.3 m
5. Find the height and base of this parallelogram
if the area is 168 square units
x+2
x
h = 12 , b = 14 units
6.
Find the area of a parallelogram if
the height is 8 cm and the base length is 10.2 cm.
Standardized Test Practice:
A
28.4 cm²
B
29.2 cm²
C
81.6 cm²
Click the mouse button or press the
Space Bar to display the answers.
D
104.4 cm²
Lesson 11-2
Areas of Triangles, Trapezoids,
and Rhombi
Objectives
• Find areas of triangles
– A = ½ bh
• Find areas of trapezoids
– A = ½ (b1 + b2)h
• Find areas of rhombi
– A = ½ d1 · d2
(note: this is the one area formula not on SOL formula sheet)
Vocabulary
• base – the “horizontal” distance of the figure
(bottom side)
• height – the “vertical” distance of the figure
• area – the amount of flat space defined by the figure
(measured in square units)
• perimeter – once around the figure
Area of Triangles, Trapezoids & Rhombi
Triangle Area
R
A = ½ * b * h = ½ * ST * RW
h is height (altitude)
b is base (┴ to h)
h
J
K
Trapezoid Area
A = ½* h* (b1 + b2) = ½ * LN * (JK + LM)
h is height (altitude)
b1 and b2 are bases (JK & LM)
(bases are parallel sides)
h
L
T
W
b1
N
S
b2
M
A
B
d1
Rhombus Area
A = ½ * d1 * d2 = ½ * AD * BC
d1 and d2 are diagonals
d2
C
D
Triangle Area Example
R
Find the area of triangle RST
h
A = ½ bh = ½ 20(h) = 10h square units
S
45°
10 W
(side opposite 45°) h = ½ hyp √2
No hypotenuse!
∆ RSW is right isosceles; so legs are equal!
h = 10
So, area = 10(10) = 100 square units
T
10
Trapezoids Area Example
Find the area of trapezoid JKLM
A = ½ (b1 + b2)h
= ½ (12 + 20)(h) = 16h square units
(side opposite 60°) h = ½ hyp √3
J 60°
20
N
14
K
h
M
12
L
h = ½ (14) √3
h = 7 √3
So, area = 16(7√3) ≈ 193.99 square units
Rhombi Area Example
A
Find the area of rhombus ABCD
A = ½ (d1 · d2)
5
= ½ (2(3) · 2(4))
= ½ (48) = 24 square units
What if we try to find the area by
adding the 4 triangles together?
A = 4 (½ bh) = 2bh
A = 2(3)(4) = 2 (12) = 24 square units!!
B
3
4
D
5
C
Find the area of quadrilateral ABCD if AC = 35, BF = 18, and DE = 10.
The area of the quadrilateral is
equal to the sum of the areas of
Area formula
Substitution
Simplify.
Answer: The area of ABCD is 490 square units.
Find the area of quadrilateral HIJK if IK = 16, HL = 5 and JM = 9
Answer:
Rhombus RSTU has an area of 64 square inches.
Find US if RT = 8 inches.
Use the formula for the
area of a rhombus and
solve for d2.
Answer:
US is 16 inches long.
Trapezoid DEFG has an area of 120 square feet.
Find the height of DEFG.
Use the formula for the area of a trapezoid and solve for h.
Answer:
The height of trapezoid DEFG is 8 feet.
a. Rhombus ABCD has an area
of 81 square centimeters.
Find BD if AC = 6 centimeters.
Answer:
27 cm
b. Trapezoid QRST has
an area of 210 square
yards. Find the height
of QRST.
Answer:
6 yd
STAINED GLASS This stained glass window is composed of 8
congruent trapezoidal shapes. The total area of the design is 72
square feet. Each trapezoid has bases of 3 and 6 feet. Find the
height of each trapezoid.
First, find the area of one trapezoid. From
Postulate 11.1, the area of each trapezoid
is the same. So, the area of each
trapezoid is 72  8 or 9 square feet.
Next, use the area formula to find the
height of each trapezoid.
Area of a trapezoid
Substitution
Add.
Multiply.
Divide each side by 4.5.
Answer:
Each trapezoid has a height of 2 feet.
INTERIOR DESIGN This window hanging is composed of 12
congruent trapezoidal shapes. The total area of the design is 216
square inches. Each trapezoid has bases of 4 and 8 inches. Find
the height of each trapezoid.
Answer:
3 in.
Summary & Homework
• Summary:
– The formula for the area of a triangle can be used
to find the areas of many different figures
– Congruent figures have equal areas
• Homework:
– pg 606-608; 13-18, 30-34