Find the height $h$ of a triangular prism if volume $V = 7.8 cm$ and base area $B = 3.4 cm$ .

Answer

$2.4267$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

B = \frac{3 \cdot a ^{2}}{4}

After substituting $B = 3.4 cm$ we have:

3.4 cm = \frac{3 \cdot a ^{2}}{4}

3.4 cm \cdot 4 = 3 \cdot a^{2}

13.6 cm = 3 \cdot a^{2}

a^{2} = \frac{13.6 cm}{3}

a^{2} = 7.852 cm

a = 7.852 cm

a \approx 2.8021

STEP 2: find height $h$

To find height $h$ use formula:

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

After substituting $a = 2.8021 cm^{0}$ we have:

h = \frac{3 \cdot 2.8021}{2}

h = \frac{4.8534}{2}

h \approx 2.4267

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Find the height h of a triangular prism if volume V=7.8cm and base area B=3.4cm.

2.4267

Find the height $h$ of a triangular prism if volume $V = 7.8 cm$ and base area $B = 3.4 cm$ .

$2.4267$