**Triangle = Flat Shape with Three Sides**

**
Basics
**s

_{1}= side 1

s

_{2}= 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 (provided by Mathematics Formula Sheet)**P = s

_{1}+ s

_{2}+ s

_{3}

A = bh

**Formulas (NOT provided by Mathematics Formula Sheet)**

s

_{1}= P – s

_{2}– s

_{3}

s

_{2}= P – s

_{1}– s

_{3}

s

_{3}= P – s

_{1}– s

_{2}

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 = s_{1} + s_{2} + s_{3}

P = 6 + 8 + 10 = 24

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

6 + 8 + 10 | 6+8+10 | P = s_{1} + s_{2} + s_{3} |

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**

A = bh

A = × 8 × 6 = 24

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

1 2 × 8 × 6 | *8*6 | A = bh |

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

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

180 – 33 – 90 | 180-33-90 | y = 180° – x – z |

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**

s_{3} = P – s_{1} – s_{2}

s_{3} = 30 – 5 – 13 = 12

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

30 – 5 – 13 | 30-5-13 | s_{3} = P – s_{1} – s_{2} |

12 | Answer | |

## Triangle |

**
Question
**A triangular sign has an area of 42 square feet and a height of 7 feet.

How long it its base?

**Answer
**12 feet

**Answer Process**

b = 2 × A ÷ h

b = 2 × 42 ÷ 7 = 12

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

2 × 42 ÷ 7 | 2*42÷7 | b = 2 × A ÷ h |

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

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

2 × 96 ÷ 8 | 2*96÷8 | h = 2 × A ÷ b |

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