Find the area $ A $ of a pyramid if side $a = 15$ and height $h = 10$.

$A = 600$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 15 $ we have:

$$ B = 15^2 $$ $$ B = 225 $$

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 = 10 $ and $ a = 15 $ we have:

$$ 10^2 + \frac{ 15^2 }{ 4 }= s^2 $$ $$ 100 + \frac{ 225 }{ 4 }= s^2 $$ $$ 100 + \frac{ 225 }{ 4 } = s^2 $$ $$ s^2 = \frac{ 625 }{ 4 } $$ $$ s = \sqrt{ \frac{ 625 }{ 4 } } $$$$ s = \frac{ 25 }{ 2 } $$

STEP 3: find lateral surface $ L $

To find lateral surface $ L $ use formula:

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

After substituting $ a = 15 $ and $ s = \frac{ 25 }{ 2 } $ we have:

$$ L = 30 \cdot \frac{ 25 }{ 2 } $$$$ L = 375 $$

STEP 4: find total surface $ A $

To find total surface $ A $ use formula:

$$ A = B + L $$

After substituting $ B = 225 $ and $ L = 375 $ we have:

$$ A = 225 + 375 $$ $$ A = 225 + 375 $$ $$ A = 600 $$

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