Find the lateral area $L$ of a pyramid if height $h = 30 cm$ and slant height $s = 32 cm$ .

Answer

$25631 cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use Pythagorean Theorem:

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

After substituting $h = 30 cm$ and $s = 32 cm$ we have:

(30 cm)^{2} + \frac{a ^{2}}{4} = (32 cm)^{2}

\frac{a ^{2}}{4} = (32 cm)^{2} - (30 cm)^{2}

\frac{a ^{2}}{4} = 1024 cm^{2} - 900 cm^{2}

a^{2} = 124 cm^{2} \cdot 4

a^{2} = 496 cm^{2}

a = 496 cm^{2}

a = 431 cm

STEP 2: find lateral surface $L$

To find lateral surface $L$ use formula:

L = 2 \cdot a \cdot s

After substituting $a = 431 cm$ and $s = 32 cm$ we have:

L = 831 cm \cdot 32 cm

L = 25631 cm^{2}

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Find the lateral area L of a pyramid if height h=30cm and slant height s=32cm.

25631​cm2

Find the lateral area $L$ of a pyramid if height $h = 30 cm$ and slant height $s = 32 cm$ .

$25631 cm^{2}$