Find the area $ A $ of a pyramid if side $a = 8$ and height $h = 5$.

$A = 166.45$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 8 $ we have:

$$ B = 8^2 $$ $$ B = 64 $$

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 = 5 $ and $ a = 8 $ we have:

$$ 5^2 + \frac{ 8^2 }{ 4 }= s^2 $$ $$ 25 + \frac{ 64 }{ 4 }= s^2 $$ $$ 25 + 16 = s^2 $$ $$ s^2 = 41 $$ $$ s = \sqrt{ 41 } $$

STEP 3: find lateral surface $ L $

To find lateral surface $ L $ use formula:

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

After substituting $ a = 8 $ and $ s = \sqrt{ 41 } $ we have:

$$ L = 16 \cdot \sqrt{ 41 } $$$$ L = 16 \sqrt{ 41 } $$

STEP 4: find total surface $ A $

To find total surface $ A $ use formula:

$$ A = B + L $$

After substituting $ B = 64 $ and $ L = 16 \sqrt{ 41 } $ we have:

$$ A = 64 + 16 \sqrt{ 41 } $$ $$ A = 64 + 16 \sqrt{ 41 } $$ $$ A = 166.45 $$

Pyramid Calculator