Find the area $A$ of a triangular prism if length $l = 15 cm$ and height $h = 4 cm$ .

Answer

$\frac{392 3}{3} cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $h = 4 cm$ we have:

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

3 \cdot a = 4 cm \cdot 2

3 \cdot a = 8 cm

a = \frac{8 cm}{3}

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

STEP 2: find area $A$

To find area $A$ use formula:

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

After substituting $a = \frac{8 3}{3} cm$ and $l = 15 cm$ we have:

A = \frac{\frac{8 3}{3} cm ^{2} 3}{2} + 3 \cdot \frac{8 3}{3} cm \cdot 15 cm

A = \frac{\frac{64}{3} cm ^{2} 3}{2} + 3 \cdot 403 cm^{2}

A = \frac{\frac{64 3}{3} cm ^{2}}{2} + 1203 cm^{2}

A = \frac{32 3}{3} cm^{2} + 1203 cm^{2}

A = \frac{392 3}{3} cm^{2}

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Find the area A of a triangular prism if length l=15cm and height h=4cm.

33923​​cm2

Find the area $A$ of a triangular prism if length $l = 15 cm$ and height $h = 4 cm$ .

$\frac{392 3}{3} cm^{2}$