Find the area $ A $ of a pyramid if side $a = 3.46$ and height $h = 4$.

$A = 42.1295$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 3.46 $ we have:

$$ B = 3.46^2 $$ $$ B = 11.9716 $$

STEP 2: find slant height $ s $

To find slant height $ s $ use Pythagorean Theorem:

$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$

After substituting $ h = 4 $ and $ a = 3.46 $ we have:

$$ 4^2 + \frac{ 3.46^2 }{ 4 }= s^2 $$ $$ 16 + \frac{ 11.9716 }{ 4 }= s^2 $$ $$ 16 + 2.9929 = s^2 $$ $$ s^2 = 18.9929 $$ $$ s = \sqrt{ 18.9929 } $$$$ s = 4.3581 $$

STEP 3: find lateral surface $ L $

To find lateral surface $ L $ use formula:

$$ L = 2 \cdot a \cdot s $$

After substituting $ a = 3.46 $ and $ s = 4.3581 $ we have:

$$ L = 6.92 \cdot 4.3581 $$$$ L = 30.1579 $$

STEP 4: find total surface $ A $

To find total surface $ A $ use formula:

$$ A = B + L $$

After substituting $ B = 11.9716 $ and $ L = 30.1579 $ we have:

$$ A = 11.9716 + 30.1579 $$ $$ A = 11.9716 + 30.1579 $$ $$ A = 42.1295 $$

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