Triangle = Flat Shape with Three Sides
Basics
s1 = side 1
s2 = side 2
s3 = side 3
x = angle x
y = angle y
z = angle z
h = height
b = base
P = Perimeter = distance along sides of triangle
A = Area = area covering surface of triangle (measured in square units)
The three angles (x, y, z) inside the triangle add up to 180°.
The right triangle pictured above, in which one of the angles measures 90°, is probably the most common type of triangle featured on the GED.
For more about the right triangle, see Pythagorean Theorem.
Formulas (Mathematics Formula Sheet)
P = s1 + s2 + s3
Formulas (NOT on Mathematics Formula Sheet)
s1 = P – s2 – s3
s2 = P – s1 – s3
s3 = P – s1 – s2
b = 2 × A ÷ h
h = 2 × A ÷ b
x + y + z = 180°
x = 180° – y – z
y = 180° – x – z
z = 180° – x – z
Question
A right triangular billboard has sides of 6 feet, 8 feet, and 10 feet, respectively. What is its perimeter?
Answer
24 feet
Answer Process
P = s1 + s2 + s3
P = 6 + 8 + 10 = 24
Input | Display | Comment |
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blinker | clears screen |
6 + 8 + 10 | 6+8+10 | P = s1 + s2 + s3 |
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24 | Answer |
Triangle |
Question
A right triangular billboard has a height of 6 feet and a base of 8 feet. What is its area?
Answer
24 square feet
Answer Process
= 24
Input | Display | Comment |
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blinker | clears screen |
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24 | Answer |
Triangle |
Question
A triangular piece of pizza has an angle x that measures 33° and an angle z that measures 90°. What is the measurement of angle y (the triangular slice of pizza’s other angle) in degrees?
Answer
57°
Answer Process
y = 180° – x – z
y = 180 – 33 – 90 = 57
Input | Display | Comment |
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blinker | clears screen |
180 – 33 – 90 | 180 – 33 – 90 | y = 180° – x – z |
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57 | Answer |
Triangle |
Question
A right triangular billboard with a perimeter of 30 feet has one side that measures 5 feet and another side that measures 13 feet. What is the length of its third side?
Answer
12 feet
Answer Process
s3 = P – s1 – s2
s3 = 30 – 5 – 13 = 12
Input | Display | Comment |
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blinker | clears screen |
30 – 5 – 13 | 30-5-13 | s3 = P – s1 – s2 |
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12 | Answer |
Triangle |
Question
A triangular sign has an area of 42 square feet and a height of 7 feet. How long is its base?
Answer
12 feet
Answer Process
b = 2 × A ÷ h
b = 2 × 42 ÷ 7 = 12
Input | Display | Comment |
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blinker | clears screen |
2 × 42 ÷ 7 | 2*42÷7 | b = 2 × A ÷ h |
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12 | Answer |
Triangle |
Question
A triangular sign has an area of 96 square feet and a base of 8 feet. How high is it?
Answer
24 feet
Answer Process
h = 2 × A ÷ b
h = 2 × 96 ÷ 8 = 24
Input | Display | Comment |
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blinker | clears screen |
2 × 96 ÷ 8 | 2*96÷8 | h = 2 × A ÷ b |
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24 | Answer |
Triangle |
Practice – Questions
1. A right triangular sign has a height of 3 feet, base of 4 feet, and hypotenuse of 5 feet. What is its perimeter?
2. A right triangular sign has a height of 3 feet, base of 4 feet, and hypotenuse of 5 feet. What is its area?
3. A triangular piece of pie has one angle that measures 47° and a second angle that measures 68°. What is the measurement of the pie’s third angle in degrees?
4. A right triangular tile with a perimeter of 34 centimeters has a base of 12 centimeters and a hypotenuse of 15 centimeters. How high is it?
5. A triangular sign has an area of 105 square feet and a height of 15 feet. How long it its base?
Practice – Answers
1. 12 feet
2. 6 square feet
3. 65°
4. 7 centimeters
5. 14 feet