Name: ________________________ Class: ___________________ Date: __________
ID: A
Area of Triangles Problem Set
Short Answer
1. Two sides of a parallelogram are 24 feet and 30
feet. The measure of the angle between these sides
is 57°. Find the area of the parallelogram, to the
nearest square foot.
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4. Gregory wants to build a garden in the shape of an
isosceles triangle with one of the congruent sides
equal to 12 yards. If the area of his garden will be
55 square yards, find, to the nearest tenth of a
degree, the three angles of the triangle.
-
2. The two sides and included angle of a
parallelogram are 18, 22, and 60°. Find its exact
area in simplest form.
-
5. A farmer has determined that a crop of strawberries
yields a yearly profit of $1.50 per square yard. If
strawberries are planted on a triangular piece of
land whose sides are 50 yards, 75 yards, and 100
yards, how much profit, to the nearest hundred
dollars, would the farmer expect to make from this
piece of land during the next harvest?
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3. A ranch in the Australian Outback is shaped like
triangle ACE, with m∠A = 42, m∠E = 103 , and
AC = 15 miles. Find the area of the ranch, to the
nearest square mile.
-
6. The triangular top of a table has two sides of 14
inches and 16 inches, and the angle between the
sides is 30°. Find the area of the tabletop, in square
inches.
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Name: ________________________
ID: A
9. In the accompanying diagram of parallelogram
ABCD, m∠A = 30, AB = 10, and AD = 6. What is
the area of parallelogram ABCD?
7. A triangular plot of land has sides that measure 5
meters, 7 meters, and 10 meters. What is the area
of this plot of land, to the nearest tenth of a square
meter?
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8. The accompanying diagram shows a triangular plot
of land that is part of Fran's garden. She needs to
change the dimensions of this part of the garden,
but she wants the area to stay the same. She
increases the length of side AC to 22.5 feet. If
angle A remains the same, by how many feet
should side AB be decreased to make the area of
the new triangular plot of land the same as the
current one?
10. The accompanying diagram shows a triangular plot
of land located in Moira’s garden.
Find the area of the plot of land, and round your
answer to the nearest hundred square feet.
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ID: A
Area of Triangles Problem Set
Answer Section
SHORT ANSWER
1. ANS:
K = absinC = 24 ⋅ 30sin57 ≈ 604
PTS: 2
REF: 061034a2
KEY: parallelograms
2. ANS:
K = absinC = 18 ⋅ 22sin60 = 396
STA: A2.A.74
TOP: Using Trigonometry to Find Area
3
= 198 3
2
PTS: 2
REF: 061234a2
KEY: Parallelograms
3. ANS:
1
a
15
=
. (15)(10.3) sin35 ≈ 44
sin103 sin 42 2
STA: A2.A.74
TOP: Using Trigonometry to Find Area
REF: 061337a2
STA: A2.A.74
TOP: Using Trigonometry to Find Area
REF: 060121b
STA: A2.A.74
TOP: Using Trigonometry to Find Area
a ≈ 10.3
PTS: 4
KEY: advanced
4. ANS:
49.8°, 65.1°, 65.1°.
PTS: 2
KEY: advanced
5. ANS:
.
2700.
PTS: 6
6. ANS:
REF: 060333b
STA: A2.A.74
TOP: Heron’s Formula
PTS: 2
REF: 080324b
KEY: without calculator
STA: A2.A.74
TOP: Using Trigonometry to Find Area
56.
1
ID: A
7. ANS:
16.2.
PTS: 6
8. ANS:
2.
REF: 060634b
STA: A2.A.74
TOP: Heron’s Formula
Side AB should be decreased from 18 to 16,
.
or by 2 feet.
PTS: 4
KEY: advanced
9. ANS:
30.
REF: 080628b
STA: A2.A.74
TOP: Using Trigonometry to Find Area
PTS: 2
REF: 010924b
KEY: parallelograms
10. ANS:
STA: A2.A.74
TOP: Using Trigonometry to Find Area
STA: A2.A.74
TOP: Heron’s Formula
8,200.
PTS: 6
REF: 060933b
2