Find the area $ A $ of a pyramid if side $a = 7$ and height $h = 11.1$.

$A = 211.9422$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 7 $ we have:

$$ B = 7^2 $$ $$ B = 49 $$

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 = 11.1 $ and $ a = 7 $ we have:

$$ 11.1^2 + \frac{ 7^2 }{ 4 }= s^2 $$ $$ 123.21 + \frac{ 49 }{ 4 }= s^2 $$ $$ 123.21 + \frac{ 49 }{ 4 } = s^2 $$ $$ s^2 = 135.46 $$ $$ s = \sqrt{ 135.46 } $$$$ s = 11.6387 $$

STEP 3: find lateral surface $ L $

To find lateral surface $ L $ use formula:

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

After substituting $ a = 7 $ and $ s = 11.6387 $ we have:

$$ L = 14 \cdot 11.6387 $$$$ L = 162.9422 $$

STEP 4: find total surface $ A $

To find total surface $ A $ use formula:

$$ A = B + L $$

After substituting $ B = 49 $ and $ L = 162.9422 $ we have:

$$ A = 49 + 162.9422 $$ $$ A = 49 + 162.9422 $$ $$ A = 211.9422 $$

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