Find the slant height $s$ of a pyramid if height $h = 12 cm$ and base diagonal $d = 10 cm$ .

Answer

$\frac{626}{2} cm$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

d = 2 \cdot a

After substituting $d = 10 cm$ we have:

10 cm = 2 \cdot a

a = \frac{10 cm}{2}

a = 52 cm

STEP 2: find slant height $s$

To find slant height $s$ use Pythagorean Theorem:

h^{2} + \frac{a ^{2}}{4} = s^{2}

After substituting $h = 12 cm$ and $a = 52 cm$ we have:

(12 cm)^{2} + \frac{( 5 2 cm ) ^{2}}{4} = s^{2}

144 cm^{2} + \frac{50 cm ^{2}}{4} = s^{2}

144 cm^{2} + \frac{25}{2} cm^{2} = s^{2}

s^{2} = \frac{313}{2} cm^{2}

s = \frac{313}{2} cm^{2}

s = \frac{626}{2} cm

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Find the slant height s of a pyramid if height h=12cm and base diagonal d=10cm.

2626​​cm

Find the slant height $s$ of a pyramid if height $h = 12 cm$ and base diagonal $d = 10 cm$ .

$\frac{626}{2} cm$