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Pythagorean Theorem and 3-D Figures. Rectangular solids. Every rectangular solid has: 6 rectangular faces: 1. 2. 3. 4. 5. 6. . 12 edges: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. . 4 diagonals: 1. 2. 3. 4.

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rectangular solids
Rectangular solids
  • Every rectangular solid has:
  • 6 rectangular faces:
  • 1.
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
slide3
12 edges:
  • 1. 2.
  • 3. 4.
  • 5. 6.
  • 7. 8.
  • 9. 10.
  • 11. 12.
slide4
4 diagonals:
  • 1.
  • 2.
  • 3.
  • 4.
  • A cube is a rectangular solid in which all edges are congruent. All faces are squares!
regular square pyramid
Regular Square Pyramid
  • KLQP is a square and is called the base.
  • J is the vertex.
  • is the altitude of the pyramid and is perpendicular to the base at its center.
  • is called the slant height and is perpendicular to a side of the base.
example 1 this box is a rectangular solid
Example 1: This box is a rectangular solid.
  • If BC = 3, what is AD?
  • If AB = 4 what is DB?
  • Must use BC = 3 to find
  • If CG =12, what is DH?
  • What is BH? AG?
  • Use DB = 5
example 2
Example 2:
  • The dimensions of a rectangular solid are 3, 5, and 7. Find the diagonal.
  • Draw a rectangular solid.
  • Does it matter where the numbers go?
  • 1st possibility
  • Find AH
  • To find AH first must find DH
  • Use DH to find AH
example 21
Example 2:
  • 2nd possibility
  • Find AH
  • To find AH first must find DH
  • Use DH to find AH
example 22
Example 2:
  • 3rd possibility
  • Find AH
  • To find AH first must find DH
  • Use DH to find AH
example 3
Example 3:
  • The square pyramid has altitude , slant height , perimeter of JKMO = 40, and PK = 13.
  • Find
  • a.) JK
  • Since it is a square pyramid,
  • the base is a square
  • A square has 4 congruent sides
  • If the perimeter is 40 then each
  • side is 10 so JK = 10
slide11
b.) PS
  • In a square pyramid, the slant
  • height bisects the base edge
  • So KS = 5
  • Use PK = 13 to find PS
  • PS = 12
slide12
C.) PR
  • In a square pyramid, the altitude
  • height bisects the base edge
  • So RS = 5
  • Use PS = 12 to find PR
in review
In review,
  • With any type of solid, you need to create right triangles that you can use the Pythagorean to find the missing length.
  • You may need to use the Pythagorean theorem more than once to find the missing length.