Name
LESSON
9-1
Date
Class
Reading Strategies
Use a Table
Use the table below to help you find areas of triangles and quadrilaterals.
Figure
Diagram
Formula
Example
Find the area of a triangle with
b 12 cm and h 4 cm.
H
triangle
1 bh
A __
2
1 (12)(4) cm2
A __
2
A 24 cm2
B
Find the height of a parallelogram
2
with A 18 in and b 9 in.
parallelogram
H
A bh
B
18 (9)h in.
h 2 in.
Find the area of a trapezoid with
b1 6 ft, b2 8 ft, and h 3 ft.
B1
trapezoid
1 (b b )h
A __
2
2 1
H
1 (6 8)(3) ft2
A __
2
A (7)(3) ft2
B2
A 21 ft2
Find the diagonal d2 of a kite with
2
A 36 cm and d1 8 cm.
rhombus
or kite
D1
D2
1d d
A __
2 1 2
1 (8)d cm
36 __
2
2
36 4d2 cm
d2 9 cm
Find each measurement.
1. area of the parallelogram
2. area of the triangle
12 cm
7 yd
9 cm
10 yd
3. base of a triangle with A 150 ft2 and h 30 ft
4. area of a rhombus with d 1 10 mm and d 2 30 mm
5. height of a trapezoid with A 60 in2, b1 3 in., and b2 7 in
6. base of a parallelogram with A 28 cm2 and h 7 cm
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
10
Holt Geometry
LESSON
9-1
Review for Mastery
Challenge
LESSON
9-1
Developing Formulas for Triangles and Quadrilaterals continued
Kite
Rhombus
d1
d1
d2
Developing Formulas for Triangles and Quadrilaterals
The measures of the bases_
of trapezoid QRST
cm and 15 cm, and
_are 21
_
cm. Legs QT and RS are extended
to
the measure of the altitude JL is 6_
_
meet at P. If M is the midpoint of QT and N is the midpoint of RS, find the
area of 䉭MNP.
Area of Rhombuses and Kites
0
d2
1d d
A __
2 1 2
1d d
A __
2 1 2
*
+
1
-
2
Find d 2 of the kite in which A 156 in .
1d d
A __
Area of a kite
2 1 2
4
Substitute 156 in2 for A and 26 in. for d1.
156 13d2
Simplify.
_
To find the measure of MN, fill in the missing parts of the following
statements.
_
midsegment
2. MN is the
Find each measurement.
8. d1 of the kite in which A 414 ft
7. the area of the rhombus
AC 14 cm
BD 10 cm
21 15
3. MN (
To find the measure of PK, fill in the missing parts of the following
statements.
d1 36 ft
9. d 2 of the rhombus in which A 90 m 2
MN
PK ____
4. ____
PL
10. d1 of the kite in which A 39 mm 2
TS
Proportionality
Reason: Triangle
JL
5.
6 mm
15 m
Reason:
d2 12 m
9-1
2
A 14a b in
7
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
32 mm
40°
*
23 mm (
9-1
4/13/07 10:45:04 AM
2. Samantha is buying stones for a 16 foot
by 3 foot walkway. She needs to buy 10%
extra for cutting stones for the corners
and ends. The stones are rectangles
7 inches long and 4 inches wide and
cost $0.97 each. About how much will
the stones cost for her walkway?
-
8
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
LESSON
,
A _1_ (PK )(MN ) _1_ (18 cm)(18 cm) 162 cm
2
2
2
Holt Geometry
Developing Formulas for Triangles and Quadrilaterals
+
Holt Geometry
Reading Strategies
Use a Table
Use the table below to help you find areas of triangles and quadrilaterals.
Figure
Diagram
Formula
Example
Find the area of a triangle with
b 12 cm and h 4 cm.
A _1_ bh
2
H
triangle
A _1_(12)(4) cm2
2
A 24 cm2
B
about $263.84
21.8 mm
Find the height of a parallelogram
with A 18 in2 and b 9 in.
4. Find the area of the kite. Round to the
nearest tenth.
3. The length of a rectangular pool is
2 feet less than twice the width. If the
2
area of the pool is 264 ft , what are
the dimensions of the pool?
parallelogram
h 2 in.
4 cm
5. A parallelogram has sides of length
30 centimeters and 18 centimeters.
One of its angles measures 58. Which
is the best estimate for the area of the
parallelogram?
2
J 672 in
7. In rhombus ABCD, the length of
_
diagonal BD is _2_ the length of
_
3
diagonal AC. If the area of the
A 21 ft2
D1
rhombus
or kite
A _1_ d1d2
2
D2
d2 9 cm
Find each measurement.
1. area of the parallelogram
2. area of the triangle
-
2
7 yd
9 cm
10 yd
#
,
A 108 cm2
.
2
3. base of a triangle with A 150 ft and h 30 ft
$
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
36 _1_(8)d2 cm
2
36 4d2 cm
12 cm
figure is 75 cm , find BD.
A 7.1 cm
B 10 cm
A _1_(6 8)(3) ft2
2
A (7)(3) ft2
Find the diagonal d2 of a kite with
2
A 36 cm and d1 8 cm.
2
8. The house is made from 7 puzzle
pieces. The pieces are triangles and
parallelograms. If the area of the chimney
is _1_ in 2, what is the area of 䉭LMN ?
8
A _1_ (b1 b2)h
2
H
B2
H 366.6 in2
F 146.6 in
2
G 293.3 in
2
Find the area of a trapezoid with
b1 6 ft, b2 8 ft, and h 3 ft.
B1
trapezoid
6. Jamie is cutting out 32 right triangles from
fabric for her quilt. The shortest side of
each triangle is 2 inches, and the longest
side is 5 inches. How much fabric will she
use to cut out all the triangles?
cm
2
cm
cm2
cm2
!
18 (9)h in.
2.3 cm
26.3 cm2
"
A bh
B
Choose the best answer.
274.8
286.2
457.9
540.0
H
8.5 cm
12 ft by 22 ft
A
B
C
D
) 3 cm
18 cm
8. Find the area of 䉭MNP.
2
Problem Solving
1. The area of trapezoid HJKL is 385 mm2.
Find LM to the nearest tenth.
JL
Two-Transversal Proportionality Theorem
18
___
Reason: Substitution Property of Equality
21
7. PK 12. the area of a rhombus in which
d1 4ab in. and d 2 7a in.
d1 4x m
Theorem
6 cm and KL _1_ (
2
MN PK
6. _______
___
TS
PK KL
d1 13 mm
11. d1 of a kite in which A 16x m2 and
d2 8 m
LESSON
Theorem
_
C
A 70 cm2
001_062_Go08an_CRF_c09.indd 7
18 cm
)2
Trapezoid Midsegment
Reason:
23 ft
of trapezoid QRST.
Midsegment
Reason: Definition of
2
B
D
3
A _1_ (PK)(MN)
2
26 in.
Divide both sides by 13.
A
,
1. Using names of segments in the diagram, write the formula for finding the area of 䉭MNP.
1 (26)d
156 __
2
2
12 in. d2
2
.
4. area of a rhombus with d 1 10 mm and d 2 30 mm
C 10.6 cm
D 15 cm
9 in2
F ___
32
2
___
G 9 in
16
9
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
H _9_ in2
2
J 9 in
2
5. height of a trapezoid with A 60 in , b1 3 in., and b2 7 in
6. base of a parallelogram with A 28 cm2 and h 7 cm
2
Holt Geometry
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
52
10
A 35 yd2
b 10 ft
A 150 mm2
h 12 in.
b 4 cm
Holt Geometry
Holt Geometry