Find the area $A$ of a triangular prism if length $l = 19 cm$ and volume $V = 4495.4 cm$ .

Answer

$902.3445$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

V = \frac{3 \cdot a ^{2} \cdot l}{4}

After substituting $V = 4495.4 cm$ and $l = 19 cm$ we have:

4495.4 cm = \frac{3 \cdot a ^{2} \cdot ( 19 cm ) ^{4}}{4}

4495.4 cm \cdot 4 = 3 \cdot a^{2} \cdot (19 cm)^{4}

17981.6 cm = 3 \cdot a^{2} \cdot (19 cm)^{4}

17981.6 cm = 193 cm \cdot a^{2}

a^{2} = \frac{17981.6 cm}{19 3 cm}

a^{2} \approx 173.9255

a \approx 173.9255

a \approx 13.1881

STEP 2: find area $A$

To find area $A$ use formula:

A = \frac{a ^{2} 3}{2} + 3 a l

After substituting $a = 13.1881 cm^{0}$ and $l = 19 cm$ we have:

A = \frac{13.188 1 ^{2} 3}{2} + 3 \cdot 13.1881 \cdot 19 cm

A = \frac{173.9255 3}{2} + 3 \cdot 250.5735 cm

A = \frac{301.2478}{2} + 751.7206 cm

A = 150.6239 + 751.7206 cm

A = 902.3445

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Find the area A of a triangular prism if length l=19cm and volume V=4495.4cm.

902.3445

Find the area $A$ of a triangular prism if length $l = 19 cm$ and volume $V = 4495.4 cm$ .

$902.3445$