Find the side $a$ of a pyramid if height $h = 13 cm$ and slant height $s = 15 cm$ .

Answer

$414 cm$

Explanation

To find side $a$ use Pythagorean Theorem:

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

After substituting $h = 13 cm$ and $s = 15 cm$ we have:

(13 cm)^{2} + \frac{a ^{2}}{4} = (15 cm)^{2}

\frac{a ^{2}}{4} = (15 cm)^{2} - (13 cm)^{2}

\frac{a ^{2}}{4} = 225 cm^{2} - 169 cm^{2}

a^{2} = 56 cm^{2} \cdot 4

a^{2} = 224 cm^{2}

a = 224 cm^{2}

a = 414 cm

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Find the side a of a pyramid if height h=13cm and slant height s=15cm.

414​cm

Find the side $a$ of a pyramid if height $h = 13 cm$ and slant height $s = 15 cm$ .

$414 cm$