Find the volume $V$ of a triangular prism if side $a = 1 cm$ and lateral $A L = \frac{3}{4} cm$ .

Answer

$\frac{1}{16} cm^{2}$

Explanation

STEP 1: find length $l$

To find length $l$ use formula:

A L = 3 \cdot a \cdot l

After substituting $A L = \frac{3}{4} cm$ and $a = 1 cm$ we have:

\frac{3}{4} cm = 3 \cdot 1 cm \cdot l

\frac{3}{4} cm = 3 cm \cdot l

l = \frac{\frac{3}{4} cm}{3 cm}

l = \frac{3}{12}

STEP 2: find volume $V$

To find volume $V$ use formula:

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

After substituting $a = 1 cm$ and $l = \frac{3}{12} cm^{0}$ we have:

V = \frac{3 \cdot 1 cm ^{2} \cdot \frac{3}{12}}{4}

V = \frac{3 cm ^{2} \cdot \frac{3}{12}}{4}

V = \frac{\frac{1}{4} cm ^{2}}{4}

V = \frac{1}{16} cm^{2}

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Find the volume V of a triangular prism if side a=1cm and lateral AL=43​​cm.

161​cm2

Find the volume $V$ of a triangular prism if side $a = 1 cm$ and lateral $A L = \frac{3}{4} cm$ .

$\frac{1}{16} cm^{2}$