AnswersFall 24 GMS Geometry Concepts and Connections BLaw of Sines (Sec 8-3)

Area and Perimeter of Triangles Answers

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1
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Trigonometric area formula: Area =

Question illustration
A
3.9 square units
B
8.4 square units
C
11.8 square units
D
17.7 square units
2
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Triangle LMN has sides measuring 7 meters and 6 meters and a perimeter of 16 meters.Heron’s formula: Area =

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A
3 square meters
B
9 square meters
C
28 square meters
D
34 square meters
3

Trigonometric area formula: Area =

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A
29 units
B
30 units
C
41 units
D
60 units
4

The area of parallelogram WXYZ is approximately 45 square units.Trigonometric area formula: Area =

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A
5 units
B
15 units
C
30 units
D
40 units
5

A spinner for a board game consists of a cardboard circle with two plastic arrows anchored to its center. The arrows are congruent isosceles triangles connected at their bases, as shown.Heron’s formula: Area =

Question illustration
A
3.9 square centimeters
B
6.7 square centimeters
C
7.7 square centimeters
D
13.4 square centimeters
6

Perimeter = 36 cmHeron’s formula: Area =

Question illustration
A
15 square centimeters
B
25 square centimeters
C
62 square centimeters
D
72 square centimeters
7

Consider the diagram and the derivation below.Given: In △ABC, AD ⊥ BCDerive a formula for the area of △ABC using angle C.

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A
bsin(C)
Option A
B
absin(C)
Option B
C
cbsin(C)
Option C
D
hbsin(C)
Option D
8

Which expressions represent the area of triangle ABC? Select three options.

A
a c sine (60 degrees)
Option A
B
One-half b c sine (60 degrees)
Option B
C
One-half a squared sine (60 degrees)
Option C
D
StartFraction a squared b sine (60 degrees) Over 2 EndFraction
Option D
E
StartFraction a b sine (60 degrees) Over 2 EndFraction
Option E
9

Which triangle’s area can be calculated using the trigonometric area formula?

A
Triangle A B C is shown. The length of A C is 28, the length of C B is 24, and the length of A B is 16.
Option A
B
Triangle D E F is shown. The length of E F is 20. Angle F D E is 34 degrees and angle D E F is 108 degrees.
Option B
C
Triangle G H J is shown. The length of G H is 17 and the length of G J is 22. Angle H J G is 47 degrees.
Option C
D
Triangle K L M is shown. The length of K L is 29 and the length of K M is 15. Angle L K M is 35 degrees.
Option D
10

The perimeter of triangle XYZ is 24 units.

Question illustration
A
14.7 square units
B
14.9 square units
C
15.0 square units
D
15.3 square units

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