Find the height $h$ of a triangular prism if length $l = 12 cm$ and lateral $A L = 360 cm$ .

Answer

$2.7566$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

A L = 3 \cdot a \cdot l

After substituting $A L = 360 cm$ and $l = 12 cm$ we have:

360 cm = 3 \cdot a \cdot (12 cm)^{4}

360 cm = 36 cm \cdot a

a = \frac{360 cm}{36 cm}

a \approx 3.1831

STEP 2: find height $h$

To find height $h$ use formula:

h = \frac{3 \cdot a}{2}

After substituting $a = 3.1831 cm^{0}$ we have:

h = \frac{3 \cdot 3.1831}{2}

h = \frac{5.5133}{2}

h \approx 2.7566

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Find the height h of a triangular prism if length l=12cm and lateral AL=360cm.

2.7566

Find the height $h$ of a triangular prism if length $l = 12 cm$ and lateral $A L = 360 cm$ .

$2.7566$