Find the height $h$ of a pyramid if side $a = 200 cm$ and lateral edge $e = 400 cm$ .

Answer

$10014 cm$

Explanation

STEP 1: find base diagonal $d$

To find base diagonal $d$ use formula:

d = 2 \cdot a

After substituting $a = 200 cm$ we have:

d = 2 \cdot 200 cm

d = 2002 cm

STEP 2: find height $h$

To find height $h$ use Pythagorean Theorem:

h^{2} + \frac{d ^{2}}{4} = e^{2}

After substituting $d = 2002 cm$ and $e = 400 cm$ we have:

h^{2} + \frac{( 200 2 cm ) ^{2}}{4} = (400 cm)^{2}

h^{2} + \frac{80000 cm ^{2}}{4} = (400 cm)^{2}

h^{2} + 20000 cm^{2} = (400 cm)^{2}

h^{2} = 160000 cm^{2} - 20000 cm^{2}

h^{2} = 140000 cm^{2}

h = 140000 cm^{2}

h = 10014 cm

This page was created using

Pyramid Calculator

About the Author

Welcome to MathPortal. This website's owner is mathematician Miloš Petrović. I designed this website and wrote all the calculators, lessons, and formulas.

If you want to contact me, probably have some questions, write me using the contact form or email me on mathhelp@mathportal.org.

Send Me A Comment

Main Navigation

Online Math Calculators

Find the height h of a pyramid if side a=200cm and lateral edge e=400cm.

10014​cm

Find the height $h$ of a pyramid if side $a = 200 cm$ and lateral edge $e = 400 cm$ .

$10014 cm$