This math topic focuses on applying the Pythagorean theorem in three dimensions, particularly related to prisms. The problems involve determining one dimension of a prism (the depth) while knowing the hypotenuse distance between two points (A to B). This topic requires understanding and manipulating the three-dimensional Pythagorean theorem to solve for the missing dimension given the total distance between two diagonal endpoints. Each question presents a different distance and set of potential depths to further challenge problem-solving skills.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Pythagorean Theorem 3D - Prism - Hypotenuse to Dimension (Full) Worksheet

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Pythagorean Theorem 3D - Prism - Hypotenuse to Dimension (Full)
1
The distance from point A to point B is 7. What is the depth?
An svg image showing a math problem
a
1
b
2
c
3
d
8
e
5
f
12
2
The distance from point A to point B is 6. What is the depth?
An svg image showing a math problem
a
3
b
12
c
2
d
10
e
4
f
13
3
The distance from point A to point B is 9. What is the depth?
An svg image showing a math problem
a
2
b
10
c
12
d
7
e
4
f
6
4
The distance from point A to point B is 9. What is the depth?
An svg image showing a math problem
a
4
b
2
c
6
d
11
e
8
f
1
5
The distance from point A to point B is 3. What is the depth?
An svg image showing a math problem
a
1
b
9
c
7
d
2
e
8
f
10
6
The distance from point A to point B is 9. What is the depth?
An svg image showing a math problem
a
10
b
12
c
3
d
4
e
5
f
2