Find the area $ A $ of a pyramid if side $a = 10$ and height $h = 12$.

$A = 360$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 10 $ we have:

$$ B = 10^2 $$ $$ B = 100 $$

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 = 12 $ and $ a = 10 $ we have:

$$ 12^2 + \frac{ 10^2 }{ 4 }= s^2 $$ $$ 144 + \frac{ 100 }{ 4 }= s^2 $$ $$ 144 + 25 = s^2 $$ $$ s^2 = 169 $$ $$ s = \sqrt{ 169 } $$$$ s = 13 $$

STEP 3: find lateral surface $ L $

To find lateral surface $ L $ use formula:

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

After substituting $ a = 10 $ and $ s = 13 $ we have:

$$ L = 20 \cdot 13 $$$$ L = 260 $$

STEP 4: find total surface $ A $

To find total surface $ A $ use formula:

$$ A = B + L $$

After substituting $ B = 100 $ and $ L = 260 $ we have:

$$ A = 100 + 260 $$ $$ A = 100 + 260 $$ $$ A = 360 $$

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