Find the lateral area $L$ of a pyramid if side $a = 8 cm$ and lateral edge $e = 8 cm$ .

Answer

$643 cm^{2}$

Explanation

STEP 1: find slant height $s$

To find slant height $s$ use Pythagorean Theorem:

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

After substituting $a = 8 cm$ and $e = 8 cm$ we have:

s^{2} + \frac{( 8 cm ) ^{2}}{4} = (8 cm)^{2}

s^{2} + \frac{64 cm ^{2}}{4} = (8 cm)^{2}

s^{2} + 16 cm^{2} = (8 cm)^{2}

s^{2} = 64 cm^{2} - 16 cm^{2}

s^{2} = 48 cm^{2}

s = 48 cm^{2}

s = 43 cm

STEP 2: find lateral surface $L$

To find lateral surface $L$ use formula:

L = 2 \cdot a \cdot s

After substituting $a = 8 cm$ and $s = 43 cm$ we have:

L = 16 cm \cdot 43 cm

L = 643 cm^{2}

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Find the lateral area L of a pyramid if side a=8cm and lateral edge e=8cm.

643​cm2

Find the lateral area $L$ of a pyramid if side $a = 8 cm$ and lateral edge $e = 8 cm$ .

$643 cm^{2}$