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Using the Pythagorean Theorem in 3-Dimensional Shapes

Using the Pythagorean Theorem in 3-Dimensional Shapes. Pythagorean Theorem Review. The Pythagorean Theorem states: in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. a 2 + b 2 = c 2 Find the length of AC in the diagram below:. c.

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Using the Pythagorean Theorem in 3-Dimensional Shapes

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  1. Using the Pythagorean Theorem in 3-Dimensional Shapes

  2. Pythagorean Theorem Review • The Pythagorean Theorem states:in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. a2 + b2 = c2 • Find the length of AC in thediagram below: c a b a2 + 52 = 132 a2 + 25 = 169 a2 = 144 a = 12

  3. 3-Dimensional Figures • How would you find the length of segment AV? • Do you see a right triangle inside the shape? • How would you find the length of segment AF? • Do you see the right triangle inside the shape? 12 m 5 m

  4. 3D Figures To Find the Diagonal of a 3D Prism To Find the slant height of a cone or pyramid • Diagonals of prisms have a different formula • (length)2+ (width)2 + (height)2 = (diagonal of prism)2 • It doesn’t matter that it is 3D, there is a right triangle hidden in the problem • The slant height is just the hypotenuse of a right triangle. • Use a2 + b2 = c2

  5. Use the Pythagorean Theorem to find the length of diagonal AF. G • AF is the diagonal going through a prism. To find AF, we use the Pythagorean Theorem differently. • To find AF we need to know the length, width and height of the prism (because it is a 3D shape, we need 3 measurements) • What is the length = AB? • What is the width = FG? • What is the height = GB? • (length)2 + (width)2 + (height)2= (diagonal of prism)2 • 62 + 22+ 32= d2 • 36 + 4 + 9 = d2 • 49 = d2 • 7 = d 6cm 6 cm 2 cm 3 cm The length of the diagonal AF is 7 cm.

  6. Use the Pythagorean Theorem to find the length of diagonal TX. • TX is the diagonal going through a prism. To find TX, we use the Pythagorean Theorem differently. • What is the length = TU? • What is the width = XW? • What is the height = UW? • (length)2 + (width)2 + (height)2= (diagonal of prism)2 • 122 + 62+ 92= d2 • 144 + 36 + 81 = d2 • 261 = d2 • = d 12 in 6 in 9 in The length of the diagonal TX is which is between 16 and 17 inches.

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