Find the area $A$ of a triangular prism if height $h = 10 cm$ and lateral $A L = 500 cm$ .

Answer

$615.4701 cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $h = 10 cm$ we have:

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

3 \cdot a = 10 cm \cdot 2

3 \cdot a = 20 cm

a = \frac{20 cm}{3}

a = \frac{20 3}{3} cm

STEP 2: find base area $B$

To find base area $B$ use formula:

B = \frac{3 \cdot a ^{2}}{4}

After substituting $a = \frac{20 3}{3} cm$ we have:

B = \frac{3 \cdot ( \frac{20 3}{3} cm ) ^{2}}{4}

B = \frac{3 \cdot \frac{400}{3} cm ^{2}}{4}

B = \frac{\frac{400 3}{3} cm ^{2}}{4}

B = \frac{100 3}{3} cm^{2}

STEP 3: find area $A$

To find area $A$ use formula:

A = 2 B + A L

After substituting $B = \frac{100 3}{3} cm^{2}$ and $A L = 500 cm$ we have:

A = 2 \cdot \frac{100 3}{3} cm^{2} + 500 cm

A = \frac{200 3}{3} cm^{2} + 500 cm

A = 615.4701 cm^{2}

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Find the area A of a triangular prism if height h=10cm and lateral AL=500cm.

615.4701cm2

Find the area $A$ of a triangular prism if height $h = 10 cm$ and lateral $A L = 500 cm$ .

$615.4701 cm^{2}$