Find the lateral edge $e$ of a pyramid if side $a = 1 cm$ and height $h = 1 cm$ .

Answer

$\frac{6}{2} cm$

Explanation

STEP 1: find base diagonal $d$

To find base diagonal $d$ use formula:

d = 2 \cdot a

After substituting $a = 1 cm$ we have:

d = 2 \cdot 1 cm

d = 2 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 $h = 1 cm$ and $d = 2 cm$ we have:

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

1 cm^{2} + \frac{2 cm ^{2}}{4} = e^{2}

1 cm^{2} + \frac{1}{2} cm^{2} = e^{2}

e^{2} = \frac{3}{2} cm^{2}

e = \frac{3}{2} cm^{2}

e = \frac{6}{2} cm

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Find the lateral edge e of a pyramid if side a=1cm and height h=1cm.

26​​cm

Find the lateral edge $e$ of a pyramid if side $a = 1 cm$ and height $h = 1 cm$ .

$\frac{6}{2} cm$