**Pyramid = Three-Dimensional Shape with Polygonal Base Connecting to a Point**

Basics

h = height

b = base = distance along a side of pyramid’s base

s = slant height= distance along pyramid’s side

Apex = point or peak to which a pyramid connects

Base = foundation of pyramid

p = perimeter of base

B = area of base

SA = Surface Area = area covering surface, including base, of pyramid (measured in square units)

LA = Lateral Area = area covering surface, excluding base, of pyramid (measured in square units)

V = Volume = space occupied by pyramid (measured in cubic units)

The pyramid pictured above, with triangular sides and a square base, is the type of pyramid probably featured most frequently on the GED. However, pyramids with bases of other polygonal shapes (triangle, pentagon, etc.) are possible.

Formulas (provided by ** Mathematics Formula Sheet**)

SA = ps + B

V = Bh

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

p = 4b (square Base)

B = b² (square Base)

LA = ps

h =

s =

Parentheses protect order of operations.

**
Question
**An ancient, square-based pyramid has a base of 600 meters, height 800 meters, and slant height 1000 meters. What is its surface area?

**Answer
**1560000 square meters

**Answer Process**

p = 4b

p = 4 × 600 = 2400

B = b²

B = 600² = 360000

SA = ps + B

SA = *2400*1000+360000 = 1560000

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

4 × 600 | 4*600 | p = 4b |

2400 | p | |

600 | 600² | B = b² |

enter | 360000 | B |

1 2 × 2400 × 1000 + 360000 |
*2400*1000+360000 | SA = ps + B |

enter | 1560000 | Answer |

## Pyramid |

**
Question
**An ancient, square-based pyramid has a base of 600 meters, height 800 meters, and slant height 1000 meters. What is its volume?

**Answer
**96000000 cubic meters

**Answer Process**

B = b²

B = 600² = 360000

V = Bh

V = *360000*800 = 96000000

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

600 | 600² | B = b² |

360000 | B | |

1 3 × 360000 × 800 |
*360000*800 | V = Bh |

96000000 | Answer | |

## Pyramid |

**
Question
**An ancient, square-based pyramid has a base of 600 meters, height 800 meters, and slant height 1000 meters. What is its lateral area?

**Answer
**1200000 square meters

**Answer Process**

p = 4b

p = 4 × 600 = 2400

LA = ps

LA = *2400*1000 = 1200000

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

4 × 600 | 4*600 | p = 4b |

2400 | p | |

1 2 × 2400 × 1000 |
*2400*1000 | LA = ps |

1200000 | Answer | |

## Pyramid |

**
Question
**An ancient, square-based pyramid has a base of 300 meters and a surface area of 309000 square meters. What is its slant height?

**Answer
**500 meters

**Answer Process
**p = 4b

p = 4 × 300 = 1200

B = b²

B = 300² = 90000

s =

s = = 500

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

4 × 300 | 4*300 | p = 4b |

1200 | p | |

300 | 300² | B = b² |

90000 | B | |

2 309000 – 9000 1200 |
s = | |

500 | Answer | |

## Pyramid |

**
Question
**An ancient, square-based pyramid has a base of 300 meters and a volume of 1200000 cubic meters. What is its height?

**Answer
**40 meters

**Answer Process**

B = b²

B = 300² = 90000

h =

h = = 40

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

300 | 300² | B = b² |

90000 | B | |

3 × 1200000 90000 | h = | |

40 | Answer | |

## Pyramid |

**
Practice – Questions
**1. An ancient, square-based pyramid has a base of 300 meters, height 400 meters, and slant height 500 meters. What is its surface area?

2. An ancient, square-based pyramid has a base of 300 meters, height 400 meters, and slant height 500 meters. What is its volume?

3. An ancient, square-based pyramid has a base of 300 meters, height 400 meters, and slant height 500 meters. What is its lateral area?

4. An ancient, square-based pyramid has a base of 600 meters and a surface area of 1560000 square meters. What is its slant height?

5. An ancient, square-based pyramid has a base of 600 meters and a volume of 96000000 cubic meters. What is its height?

**
Practice – Answers
**1. 390000 square meters

2. 12000000 cubic meters

3. 300000 square meters

4. 1000 meters

5. 800 meters