Find the volume $V$ of a triangular prism if length $l = 13 cm$ and height $h = 8 cm$ .

Answer

$\frac{832 3}{3} cm^{3}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $h = 8 cm$ we have:

8 cm = \frac{3 \cdot a}{2}

3 \cdot a = 8 cm \cdot 2

3 \cdot a = 16 cm

a = \frac{16 cm}{3}

a = \frac{16 3}{3} cm

STEP 2: find volume $V$

To find volume $V$ use formula:

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

After substituting $a = \frac{16 3}{3} cm$ and $l = 13 cm$ we have:

V = \frac{3 \cdot \frac{16 3}{3} cm ^{2} \cdot 13 cm}{4}

V = \frac{\frac{256 3}{3} cm ^{2} \cdot 13 cm}{4}

V = \frac{\frac{3328 3}{3} cm ^{3}}{4}

V = \frac{832 3}{3} cm^{3}

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Find the volume V of a triangular prism if length l=13cm and height h=8cm.

38323​​cm3

Find the volume $V$ of a triangular prism if length $l = 13 cm$ and height $h = 8 cm$ .

$\frac{832 3}{3} cm^{3}$