Find the area $ A $ of a pyramid if side $a = 7.8$ and height $h = 11.7$.

$A = 253.233$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 7.8 $ we have:

$$ B = 7.8^2 $$ $$ B = 60.84 $$

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 = 11.7 $ and $ a = 7.8 $ we have:

$$ 11.7^2 + \frac{ 7.8^2 }{ 4 }= s^2 $$ $$ 136.89 + \frac{ 60.84 }{ 4 }= s^2 $$ $$ 136.89 + 15.21 = s^2 $$ $$ s^2 = 152.1 $$ $$ s = \sqrt{ 152.1 } $$$$ s = 12.3329 $$

STEP 3: find lateral surface $ L $

To find lateral surface $ L $ use formula:

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

After substituting $ a = 7.8 $ and $ s = 12.3329 $ we have:

$$ L = 15.6 \cdot 12.3329 $$$$ L = 192.393 $$

STEP 4: find total surface $ A $

To find total surface $ A $ use formula:

$$ A = B + L $$

After substituting $ B = 60.84 $ and $ L = 192.393 $ we have:

$$ A = 60.84 + 192.393 $$ $$ A = 60.84 + 192.393 $$ $$ A = 253.233 $$

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