Find the area $ A $ of a pyramid if side $a = 140$ and height $h = 79.8$.

$A = 49322.2869$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 140 $ we have:

$$ B = 140^2 $$ $$ B = 19600 $$

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 = 79.8 $ and $ a = 140 $ we have:

$$ 79.8^2 + \frac{ 140^2 }{ 4 }= s^2 $$ $$ 6368.04 + \frac{ 19600 }{ 4 }= s^2 $$ $$ 6368.04 + 4900 = s^2 $$ $$ s^2 = 11268.04 $$ $$ s = \sqrt{ 11268.04 } $$$$ s = 106.151 $$

STEP 3: find lateral surface $ L $

To find lateral surface $ L $ use formula:

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

After substituting $ a = 140 $ and $ s = 106.151 $ we have:

$$ L = 280 \cdot 106.151 $$$$ L = 29722.2869 $$

STEP 4: find total surface $ A $

To find total surface $ A $ use formula:

$$ A = B + L $$

After substituting $ B = 19600 $ and $ L = 29722.2869 $ we have:

$$ A = 19600 + 29722.2869 $$ $$ A = 19600 + 29722.2869 $$ $$ A = 49322.2869 $$

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