Find the lateral edge $e$ of a pyramid if side $a = 600 cm$ and height $h = 300 cm$ .

Answer

$3003 cm$

Explanation

STEP 1: find base diagonal $d$

To find base diagonal $d$ use formula:

d = 2 \cdot a

After substituting $a = 600 cm$ we have:

d = 2 \cdot 600 cm

d = 6002 cm

STEP 2: find lateral edge $e$

To find lateral edge $e$ use Pythagorean Theorem:

h^{2} + \frac{d ^{2}}{4} = e^{2}

After substituting $h = 300 cm$ and $d = 6002 cm$ we have:

(300 cm)^{2} + \frac{( 600 2 cm ) ^{2}}{4} = e^{2}

90000 cm^{2} + \frac{720000 cm ^{2}}{4} = e^{2}

90000 cm^{2} + 180000 cm^{2} = e^{2}

e^{2} = 270000 cm^{2}

e = 270000 cm^{2}

e = 3003 cm

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Find the lateral edge e of a pyramid if side a=600cm and height h=300cm.

3003​cm

Find the lateral edge $e$ of a pyramid if side $a = 600 cm$ and height $h = 300 cm$ .

$3003 cm$