Find the lateral area $L$ of a pyramid if lateral edge $e = 10 cm$ and base diagonal $d = 12 cm$ .

Answer

$2441 cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

d = 2 \cdot a

After substituting $d = 12 cm$ we have:

12 cm = 2 \cdot a

a = \frac{12 cm}{2}

a = 62 cm

STEP 2: find slant height $s$

To find slant height $s$ use Pythagorean Theorem:

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

After substituting $a = 62 cm$ and $e = 10 cm$ we have:

s^{2} + \frac{( 6 2 cm ) ^{2}}{4} = (10 cm)^{2}

s^{2} + \frac{72 cm ^{2}}{4} = (10 cm)^{2}

s^{2} + 18 cm^{2} = (10 cm)^{2}

s^{2} = 100 cm^{2} - 18 cm^{2}

s^{2} = 82 cm^{2}

s = 82 cm^{2}

s = 82 cm

STEP 3: find lateral surface $L$

To find lateral surface $L$ use formula:

L = 2 \cdot a \cdot s

After substituting $a = 62 cm$ and $s = 82 cm$ we have:

L = 122 cm \cdot 82 cm

L = 2441 cm^{2}

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Find the lateral area L of a pyramid if lateral edge e=10cm and base diagonal d=12cm.

2441​cm2

Find the lateral area $L$ of a pyramid if lateral edge $e = 10 cm$ and base diagonal $d = 12 cm$ .

$2441 cm^{2}$