Find the lateral area $L$ of a pyramid if side $a = 6 cm$ and height $h = 14 cm$ .

Answer

$12205 cm^{2}$

Explanation

STEP 1: find slant height $s$

To find slant height $s$ use Pythagorean Theorem:

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

After substituting $h = 14 cm$ and $a = 6 cm$ we have:

(14 cm)^{2} + \frac{( 6 cm ) ^{2}}{4} = s^{2}

196 cm^{2} + \frac{36 cm ^{2}}{4} = s^{2}

196 cm^{2} + 9 cm^{2} = s^{2}

s^{2} = 205 cm^{2}

s = 205 cm^{2}

s = 205 cm

STEP 2: find lateral surface $L$

To find lateral surface $L$ use formula:

L = 2 \cdot a \cdot s

After substituting $a = 6 cm$ and $s = 205 cm$ we have:

L = 12 cm \cdot 205 cm

L = 12205 cm^{2}

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Find the lateral area L of a pyramid if side a=6cm and height h=14cm.

12205​cm2

Find the lateral area $L$ of a pyramid if side $a = 6 cm$ and height $h = 14 cm$ .

$12205 cm^{2}$