Find the area $A$ of a triangular prism if length $l = 24 cm$ and lateral $A L = 500 cm$ .

Answer

$163.3862$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

A L = 3 \cdot a \cdot l

After substituting $A L = 500 cm$ and $l = 24 cm$ we have:

500 cm = 3 \cdot a \cdot (24 cm)^{4}

500 cm = 72 cm \cdot a

a = \frac{500 cm}{72 cm}

a \approx 2.2105

STEP 2: find area $A$

To find area $A$ use formula:

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

After substituting $a = 2.2105 cm^{0}$ and $l = 24 cm$ we have:

A = \frac{2.210 5 ^{2} 3}{2} + 3 \cdot 2.2105 \cdot 24 cm

A = \frac{4.8862 3}{2} + 3 \cdot 53.0515 cm

A = \frac{8.4632}{2} + 159.1546 cm

A = 4.2316 + 159.1546 cm

A = 163.3862

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Find the area A of a triangular prism if length l=24cm and lateral AL=500cm.

163.3862

Find the area $A$ of a triangular prism if length $l = 24 cm$ and lateral $A L = 500 cm$ .

$163.3862$