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Space Diagonal

Space Diagonal. The Pythagorean Theorem in 3D. In a rectangular prism, a space diagona l is a line that goes from a vertex of the prism , through the center of the prism to the opposite vertex. aka, ‘stick in the box’. A rectangular prism has 4 space diagonals. Space Diagonal.

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Space Diagonal

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  1. Space Diagonal The Pythagorean Theorem in 3D

  2. In a rectangular prism, a space diagonal is a line that goes from a vertex of the prism, through the center of the prism to the opposite vertex. aka, ‘stick in the box’ A rectangular prism has 4 space diagonals.

  3. Space Diagonal The Pythagorean Theorem is useful when we need to find the length of a space diagonal in a rectangular prism. Side c is the space diagonal.

  4. Finding The Length Of A Space Diagonal. H G E F 16cm D C 12cm C 28cm A B 12 A 28 Look at the rectangular prism below: It is our task to calculate the length of the space diagonal AG which runs through the space inside the rectangular prism. • Start by considering the triangle ABC. (2) Calculate the length of AC. AC ≈ 30.5cm B

  5. H G E 16cm F G D 16 C A 12cm 30.5cm 30.5 28cm A B Now look at the box again. (3) Now consider triangle ACG. (4) Calculate the length of AG. C AG = AG = 34.4cm

  6. OR OR OR OR OR OR OR OR OR

  7. A diagonal of a three-dimensional figure connects two vertices of two different faces. Diagonal d of a rectangular prism is shown in the diagram. By the Pythagorean Theorem, l2 + w2 = x2 and x2 + h2 = d2. Using substitution,d2 =l2 + w2 + h2.

  8. d c b Pythagorean Theorem2D vs 3D

  9. The Space Diagonal d2 = l2 + w2 + h2.

  10. H G E F 16cm D C 12cm A 28cm B Space DiagonalPythagoras In 3D Shapes.

  11. (1) (2) 23cm 12m 17cm 3m 26cm 4m What Goes In The Box ? Calculate the lengths of the space diagonals in the rectangular prisms below:

  12. Using the Pythagorean Theorem in Three Dimensions Find the length of the space diagonal of a 6 cm by 8 cm by 10 cm rectangular prism Substitute Simplify

  13. Using the Pythagorean Theorem in Three Dimensions Find the height of a rectangular prism with a 12 in. by 7 in. base and a space diagonal of 15 in. Substitute Square both sides of the equation. Simplify. 225 = 144 + 49 + h2 Solve for h2. h2 = 32 Take the square root of both sides.

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