Name ________________________________________ Date __________________ Class__________________
LESSON
9-1
Reteach
Developing Formulas for Triangles and Quadrilaterals
Area of Triangles and Quadrilaterals
Parallelogram
Triangle
A=
A = bh
Trapezoid
1
bh
2
A=
1
( b1 + b2 ) h
2
Find the perimeter of the rectangle in which A = 27 mm2.
Step 1
Find the height.
A = bh
Area of a rectangle
27 = 3h
Substitute 27 for A and 3 for b.
9 mm = h
Step 2
Divide both sides by 3.
Use the base and the height to find the perimeter.
P = 2b + 2h
Perimeter of a rectangle
P = 2(3) + 2(9) = 24 mm
Substitute 3 for b and 9 for h.
Find each measurement.
1. the area of the parallelogram
2. the base of the rectangle in which
A = 136 mm2
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3. the area of the trapezoid
4. the height of the triangle in which
A = 192 cm2
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6. b2 of a trapezoid in which A = 5 ft2,
h = 2 ft, and b1 = 1 ft
5. the perimeter of a rectangle in which
A = 154 in2 and h = 11 in.
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________________________________________
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9-6
Holt Geometry
Name ________________________________________ Date __________________ Class__________________
LESSON
9-1
Reteach
Developing Formulas for Triangles and Quadrilaterals continued
Area of Rhombuses and Kites
Rhombus
A=
Kite
1
d1d 2
2
A=
1
d1d 2
2
Find d2 of the kite in which A = 156 in2.
A=
156 =
1
d1d 2
2
Area of a kite
1
( 26 ) d2
2
Substitute 156 in2 for A and 26 in. for d1.
156 = 13d2
12 in. = d2
Simplify.
Divide both sides by 13.
Find each measurement.
8. d1 of the kite in which A = 414 ft2
7. the area of the rhombus
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9. d2 of the rhombus in which A = 90 m2
10. d1 of the kite in which A = 39 mm2
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11. d1 of a kite in which A = 16x m2 and
d2 = 8 m
12. the area of a rhombus in which
d1 = 4ab in. and d2 = 7a in.
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________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
9-7
Holt Geometry
7. 〈7, −3〉
8. 19
9. 5
10.
3.
58 , or 7.6
11. 5 58 , or 38.1
12. 0.5
13. 60°
14. 45°
12
cm
x
4. b1 = x in.
5. A = 660 mm2
6. A = (45a + 18ac) km2
7. P = 30.4 yd
15. 143°
8. A = (xy − 2x + 4y − 8) m2
16. They are perpendicular. If the dot product
is 0, then the numerator of the expression
r is
equals 0, and the value of the
r s
entire expression is 0. A calculator tells
us that cos−10 = 90°.
9. d2 = 4a ft
Practice C
1. Possible answer: Draw a segment
showing the height from B to AD and
label it h. The area of a parallelogram is
bh. Since b is known and h = c sin A, a
formula for the area of the parallelogram
is A = bc sin A.
Problem Solving
1. 23°
2. 13 units
3. 〈4.9, 0.5〉
4. 4.9 mi/h
5. 6° or N 84° E
6. C
7. F
8. C
2. Possible answer: A rectangle is a
parallelogram in which the measure of
each angle is 90°. sin 90° = 1. So A = bc
sin A becomes A = bc, the product of the
length and the width of the rectangle.
9. H
3. A ≈ 79.9 mm2
Reading Strategies
2
1. Equal
2. 〈3, 8〉
5. A ≈ 177.5 mi
3. 69°
4. 5
7. Possible answer:
5. 6.3
6. 5.1
4. b2 ≈ 6.4 in.
6. x ≈ 60.3
7. 〈−3, 1〉
LESSON 9-1
Practice A
1. triangle
2.
1
d1d 2
2
Reteach
1. A = 60 in2
3. areas
3. A = 91 m
4. parallelogram or rectangle
5. P = 50 in.
5.
2. b = 17 mm
2
1
(b1 + b2)h
2
8. A = 567 mm2
7. A = 70 cm
8. d1 = 36 ft
9. d2 = 12 m
10. d1 = 13 mm
11. d1 = 4x m
2
9. h = 30 ft
10. A = 30 km
12. A = 14a2b in2
Challenge
11. d2 = 9 yd
1. A =
Practice B
1. P = (4x + 2y) mi
2
6. b2 = 4 ft
2
6. A = 48 m2
7. b = 3 in.
4. h = 16 cm
1
(PK)(MN)
2
2. midsegment; Midsegment
2
2
2
2. A = (a − b) = (a − 2ab + b ) ft
3. 21 + 15; 18 cm; Trapezoid Midsegment
4. PL TS; Proportionality
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A16
Holt Geometry