Find the slant height $s$ of a pyramid if height $h = 6 cm$ and lateral edge $e = 10 cm$ .

Answer

$217 cm$

Explanation

STEP 1: find base diagonal $d$

To find base diagonal $d$ use Pythagorean Theorem:

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

After substituting $h = 6 cm$ and $e = 10 cm$ we have:

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

\frac{d ^{2}}{4} = (10 cm)^{2} - (6 cm)^{2}

\frac{d ^{2}}{4} = 100 cm^{2} - 36 cm^{2}

d^{2} = 64 cm^{2} \cdot 4

d^{2} = 256 cm^{2}

d = 256 cm^{2}

d = 16 cm

STEP 2: find side $a$

To find side $a$ use formula:

d = 2 \cdot a

After substituting $d = 16 cm$ we have:

16 cm = 2 \cdot a

a = \frac{16 cm}{2}

a = 82 cm

STEP 3: find slant height $s$

To find slant height $s$ use Pythagorean Theorem:

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

After substituting $h = 6 cm$ and $a = 82 cm$ we have:

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

36 cm^{2} + \frac{128 cm ^{2}}{4} = s^{2}

36 cm^{2} + 32 cm^{2} = s^{2}

s^{2} = 68 cm^{2}

s = 68 cm^{2}

s = 217 cm

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Find the slant height s of a pyramid if height h=6cm and lateral edge e=10cm.

217​cm

Find the slant height $s$ of a pyramid if height $h = 6 cm$ and lateral edge $e = 10 cm$ .

$217 cm$