Find the lateral edge $e$ of a pyramid if height $h = 24 cm$ and slant height $s = 25 cm$ .

Answer

$674 cm$

Explanation

STEP 1: find side $a$

To find side $a$ use Pythagorean Theorem:

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

After substituting $h = 24 cm$ and $s = 25 cm$ we have:

(24 cm)^{2} + \frac{a ^{2}}{4} = (25 cm)^{2}

\frac{a ^{2}}{4} = (25 cm)^{2} - (24 cm)^{2}

\frac{a ^{2}}{4} = 625 cm^{2} - 576 cm^{2}

a^{2} = 49 cm^{2} \cdot 4

a^{2} = 196 cm^{2}

a = 196 cm^{2}

a = 14 cm

STEP 2: find lateral edge $e$

To find lateral edge $e$ use Pythagorean Theorem:

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

After substituting $s = 25 cm$ and $a = 14 cm$ we have:

(25 cm)^{2} + \frac{( 14 cm ) ^{2}}{4} = e^{2}

625 cm^{2} + \frac{196 cm ^{2}}{4} = e^{2}

625 cm^{2} + 49 cm^{2} = e^{2}

e^{2} = 674 cm^{2}

e = 674 cm^{2}

e = 674 cm

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Find the lateral edge e of a pyramid if height h=24cm and slant height s=25cm.

674​cm

Find the lateral edge $e$ of a pyramid if height $h = 24 cm$ and slant height $s = 25 cm$ .

$674 cm$