STEP 1: find base area $ B $
To find base area $ B $ use formula:
$$ B = a^2 $$After substituting $ a = 70 $ we have:
$$ B = 70^2 $$ $$ B = 4900 $$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 = 140 $ and $ a = 70 $ we have:
$$ 140^2 + \frac{ 70^2 }{ 4 }= s^2 $$ $$ 19600 + \frac{ 4900 }{ 4 }= s^2 $$ $$ 19600 + 1225 = s^2 $$ $$ s^2 = 20825 $$ $$ s = \sqrt{ 20825 } $$$$ s = 35 \sqrt{ 17 } $$STEP 3: find lateral surface $ L $
To find lateral surface $ L $ use formula:
$$ L = 2 \cdot a \cdot s $$After substituting $ a = 70 $ and $ s = 35 \sqrt{ 17 } $ we have:
$$ L = 140 \cdot 35 \sqrt{ 17 } $$$$ L = 4900 \sqrt{ 17 } $$STEP 4: find total surface $ A $
To find total surface $ A $ use formula:
$$ A = B + L $$After substituting $ B = 4900 $ and $ L = 4900 \sqrt{ 17 } $ we have:
$$ A = 4900 + 4900 \sqrt{ 17 } $$ $$ A = 4900 + 4900 \sqrt{ 17 } $$ $$ A = 25103.2176 $$