Question

Find the area $A$ of a triangular prism if volume $V = 1.7918 cm$ and base area $B = 3.4 cm$ .

Answer

$11.2302$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $B = 3.4 cm$ we have:

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

3.4 cm \cdot 4 = 3 \cdot a^{2}

13.6 cm = 3 \cdot a^{2}

a^{2} = \frac{13.6 cm}{3}

a^{2} = 7.852 cm

a = 7.852 cm

a \approx 2.8021

STEP 2: find length $l$

To find length $l$ use formula:

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

After substituting $V = 1.7918 cm$ and $a = 2.8021 cm^{0}$ we have:

1.7918 cm = \frac{3 \cdot 2.802 1 ^{2} \cdot l}{4}

1.7918 cm \cdot 4 = 3 \cdot 2.802 1^{2} \cdot l

7.1672 cm = 3 \cdot 2.802 1^{2} \cdot l

7.1672 cm = 13.6 \cdot l

l = \frac{7.1672 cm}{13.6}

l = 0.527 cm

STEP 3: find area $A$

To find area $A$ use formula:

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

After substituting $a = 2.8021 cm^{0}$ and $l = 0.527 cm$ we have:

A = \frac{2.802 1 ^{2} 3}{2} + 3 \cdot 2.8021 \cdot 0.527 cm

A = \frac{7.852 3}{2} + 3 \cdot 1.4767 cm

A = \frac{13.6}{2} + 4.4302 cm

A = 6.8 + 4.4302 cm

A = 11.2302

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