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.
oL=4W=6H=3
o 42 + 62 + 32
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 302 + 302 + 102
o 900 + 900 + 100
o 1900
1900 = 43.9 ft
o
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 72 + 92 + 62
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 122 + 92 + 82
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 242 + 102 + 82
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 102 + 102 + 102
o 100 + 100 + 100
o 300
o 300 = 17.3 in