STEP 1: find base area $ B $
To find base area $ B $ use formula:
$$ B = a^2 $$After substituting $ a = 12 $ we have:
$$ B = 12^2 $$ $$ B = 144 $$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 = 14.83 $ and $ a = 12 $ we have:
$$ 14.83^2 + \frac{ 12^2 }{ 4 }= s^2 $$ $$ 219.9289 + \frac{ 144 }{ 4 }= s^2 $$ $$ 219.9289 + 36 = s^2 $$ $$ s^2 = 255.9289 $$ $$ s = \sqrt{ 255.9289 } $$$$ s = 15.9978 $$STEP 3: find lateral surface $ L $
To find lateral surface $ L $ use formula:
$$ L = 2 \cdot a \cdot s $$After substituting $ a = 12 $ and $ s = 15.9978 $ we have:
$$ L = 24 \cdot 15.9978 $$$$ L = 383.9467 $$STEP 4: find total surface $ A $
To find total surface $ A $ use formula:
$$ A = B + L $$After substituting $ B = 144 $ and $ L = 383.9467 $ we have:
$$ A = 144 + 383.9467 $$ $$ A = 144 + 383.9467 $$ $$ A = 527.9467 $$