Find the area $ A $ of a pyramid if side $a = 19.9$ and height $h = 8.2$.

$A = 909.1715$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 19.9 $ we have:

$$ B = 19.9^2 $$ $$ B = 396.01 $$

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 = 8.2 $ and $ a = 19.9 $ we have:

$$ 8.2^2 + \frac{ 19.9^2 }{ 4 }= s^2 $$ $$ 67.24 + \frac{ 396.01 }{ 4 }= s^2 $$ $$ 67.24 + 99.0025 = s^2 $$ $$ s^2 = 166.2425 $$ $$ s = \sqrt{ 166.2425 } $$$$ s = 12.8935 $$

STEP 3: find lateral surface $ L $

To find lateral surface $ L $ use formula:

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

After substituting $ a = 19.9 $ and $ s = 12.8935 $ we have:

$$ L = 39.8 \cdot 12.8935 $$$$ L = 513.1615 $$

STEP 4: find total surface $ A $

To find total surface $ A $ use formula:

$$ A = B + L $$

After substituting $ B = 396.01 $ and $ L = 513.1615 $ we have:

$$ A = 396.01 + 513.1615 $$ $$ A = 396.01 + 513.1615 $$ $$ A = 909.1715 $$

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