Find the length $l$ of a triangular prism if side $a = 6 cm$ and area $A = 229.2 cm$ .

Answer

$11.0013$

Explanation

To find length $l$ use formula:

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

After substituting $A = 229.2 cm$ and $a = 6 cm$ we have:

229.2 cm = \frac{6 cm ^{2} 3}{2} + 3 \cdot 6 cm \cdot l

229.2 cm = \frac{36 cm ^{2} 3}{2} + 18 cm \cdot l

2 \cdot 229.2 cm = 363 cm^{2} + 2 \cdot 18 cm \cdot l

458.4 cm = 363 cm^{2} + 36 cm \cdot l

36 cm \cdot l = 458.4 cm - 363 cm^{2}

l = \frac{458.4 cm - 36 3 cm ^{2}}{36 cm}

l = \frac{396.0462 cm}{36 cm}

l = 11.0013

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Find the length l of a triangular prism if side a=6cm and area A=229.2cm.

11.0013

Find the length $l$ of a triangular prism if side $a = 6 cm$ and area $A = 229.2 cm$ .

$11.0013$