Pythagorean Theorem and Rectangular Prisms

Learning Target

• I can solve real-world and mathematical problems using the Pythagorean Theorem to find a diagonal or a rectangular prism.

Pythagorean Theorem and Rectangular Prisms • • Just like the Pythagorean Theorem, we can use a formula to easily find the length of a diagonal.

Copy the following equation: –

Pythagorean Theorem and Rectangular Prisms • A child’s shoe box measures 4” x 6” x 3”. What is the longest pencil you could fit into this box? If possible, draw a diagram to show the pencil’s position.

o L = 4 W = 6 H = 3 o 4 2 + 6 2 + 3 2 o 16 + 36 + 9 o 61 o 61 = 7.8”

Pythagorean Theorem and Rectangular Prisms • A fly was sitting on the ground in the back left corner of your classroom. He flew to the ceiling in the opposite corner of the room. How far did he fly if he if the room is 30 feet by 30 feet by 10 feet?

o L = 30 W = 30 H = 10 o 30 2 + 30 2 + 10 2 o 900 + 900 + 100 o o 1900 1900 = 43.9 ft

Pythagorean Theorem and Rectangular Prisms • Essentially, when working these problems, we are finding the diagonal from top to bottom of a rectangular prim.

Pythagorean Theorem and Rectangular Prisms • Find the diagonal from top to bottom for a rectangular prism with a length of 7 m, a width of 9 m and a height of 6 m.

o 7 2 + 9 2 + 6 2 o 49 + 81 + 36 o 166 o 166 = 12.9 m

Pythagorean Theorem and Rectangular Prisms • Find the diagonal from top to bottom for a rectangular prism with a length of 12 in, a width of 9 in and a height of 8 in.

o 12 2 + 9 2 + 8 2 o 144 + 81 + 64 o 289 o 289 = 17 in

Pythagorean Theorem and Rectangular Prisms • With your team, find the diagonal from top to bottom for the following rectangular prisms – L = 24 cm, W = 10 cm, H = 8 cm o 24 2 + 10 2 + 8 2 o 576 + 100 + 64 o 740 o 740 = 27.2 cm

Pythagorean Theorem and Rectangular Prisms • With your team, find the diagonal from top to bottom for the following rectangular prisms – L = 10 in, W = 10 in, H = 10 in o 10 2 + 10 2 + 10 2 o 100 + 100 + 100 o 300 o 300 = 17.3 in