Pythagorean theorem and 3 d figures
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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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Pythagorean Theorem and 3-D Figures

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Pythagorean theorem and 3 d figures

Pythagorean Theorem and 3-D Figures


Rectangular solids

Rectangular solids

  • Every rectangular solid has:

  • 6 rectangular faces:

  • 1.

  • 2.

  • 3.

  • 4.

  • 5.

  • 6.


Pythagorean theorem and 3 d figures

  • 12 edges:

  • 1. 2.

  • 3. 4.

  • 5. 6.

  • 7. 8.

  • 9. 10.

  • 11. 12.


Pythagorean theorem and 3 d figures

  • 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


Pythagorean theorem and 3 d figures

  • b.) PS

  • In a square pyramid, the slant

  • height bisects the base edge

  • So KS = 5

  • Use PK = 13 to find PS

  • PS = 12


Pythagorean theorem and 3 d figures

  • 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.


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