Find the area $ A $ of a pyramid if side $a = 24$ and height $h = 16$.

$A = 1536$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 24 $ we have:

$$ B = 24^2 $$ $$ B = 576 $$

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 = 16 $ and $ a = 24 $ we have:

$$ 16^2 + \frac{ 24^2 }{ 4 }= s^2 $$ $$ 256 + \frac{ 576 }{ 4 }= s^2 $$ $$ 256 + 144 = s^2 $$ $$ s^2 = 400 $$ $$ s = \sqrt{ 400 } $$$$ s = 20 $$

STEP 3: find lateral surface $ L $

To find lateral surface $ L $ use formula:

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

After substituting $ a = 24 $ and $ s = 20 $ we have:

$$ L = 48 \cdot 20 $$$$ L = 960 $$

STEP 4: find total surface $ A $

To find total surface $ A $ use formula:

$$ A = B + L $$

After substituting $ B = 576 $ and $ L = 960 $ we have:

$$ A = 576 + 960 $$ $$ A = 576 + 960 $$ $$ A = 1536 $$

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