If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

8th grade

Course: 8th grade > Unit 5

Lesson 4: Pythagorean theorem application
Math
8th grade
Geometry
Pythagorean theorem application
© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

Pythagorean theorem in 3D

Google Classroom
You might need: Calculator

Problem

Each vertical cross-section of the triangular prism shown below is an isosceles triangle.
A triangular prism with a vertical height of h units, a base of six units, and a slant height of three square root two units.
What is the vertical height, h, of the triangular prism?
Round your answer to the nearest tenth.
The height is
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
units.
Stuck?
Stuck?