Find the height $h$ of a pyramid if slant height $s = 90.3 cm$ and base diagonal $d = 20.4 cm$ .

Answer

$90.0115 cm$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

d = 2 \cdot a

After substituting $d = 20.4 cm$ we have:

20.4 cm = 2 \cdot a

a = \frac{20.4 cm}{2}

a \approx 14.425 cm

STEP 2: find height $h$

To find height $h$ use Pythagorean Theorem:

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

After substituting $a = 14.425 cm$ and $s = 90.3 cm$ we have:

h^{2} + \frac{( 14.425 cm ) ^{2}}{4} = (90.3 cm)^{2}

h^{2} + \frac{208.08 cm ^{2}}{4} = (90.3 cm)^{2}

h^{2} + 52.02 cm^{2} = (90.3 cm)^{2}

h^{2} = 8154.09 cm^{2} - 52.02 cm^{2}

h^{2} = 8102.07 cm^{2}

h = 8102.07 cm^{2}

h = 90.0115 cm

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Find the height h of a pyramid if slant height s=90.3cm and base diagonal d=20.4cm.

90.0115cm

Find the height $h$ of a pyramid if slant height $s = 90.3 cm$ and base diagonal $d = 20.4 cm$ .

$90.0115 cm$