AnswersOH-Geometry BArea and Perimeter of Triangles

Area and Perimeter of Triangles Answers

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

Question illustration
A
bsin(C)
Option A
B
absin(C)
Option B
C
cbsin(C)
Option C
D
hbsin(C)
Option D
2
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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
3

Lila made a triangular flag to cheer on her favorite sports team. The perimeter of the flag is 20 inches.Heron’s formula: Area =

Question illustration
A
15 square inches
B
76 square inches
C
186 square inches
D
215 square inches
4

Trigonometric area formula: Area =

Question illustration
A
29 units
B
30 units
C
41 units
D
60 units
5

Heron’s formula: Area =

Question illustration
A
17.75 square units
B
81.33 square units
C
372.71 square units
D
957.74 square units
6

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
7

Heron’s formula: Area =

Question illustration
A
2 square meters
B
7 square meters
C
20 square meters
D
78 square meters
8

What is the area of triangle ABC? Round to the nearest tenth of a square unit.

Question illustration
A
54.9 square units
B
58.8 square units
C
61.8 square units
D
64.1 square units
9

Jace ordered a banner in the shape of a parallelogram from a print shop.Heron’s formula: Area =

Question illustration
A
$41.95
B
$46.14
C
$83.90
D
$92.30
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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