Find the area $ A $ of a pyramid if side $a = 2.7$ and height $h = 2$.

$A = 20.3201$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 2.7 $ we have:

$$ B = 2.7^2 $$ $$ B = 7.29 $$

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 = 2 $ and $ a = 2.7 $ we have:

$$ 2^2 + \frac{ 2.7^2 }{ 4 }= s^2 $$ $$ 4 + \frac{ 7.29 }{ 4 }= s^2 $$ $$ 4 + 1.8225 = s^2 $$ $$ s^2 = 5.8225 $$ $$ s = \sqrt{ 5.8225 } $$$$ s = 2.413 $$

STEP 3: find lateral surface $ L $

To find lateral surface $ L $ use formula:

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

After substituting $ a = 2.7 $ and $ s = 2.413 $ we have:

$$ L = 5.4 \cdot 2.413 $$$$ L = 13.0301 $$

STEP 4: find total surface $ A $

To find total surface $ A $ use formula:

$$ A = B + L $$

After substituting $ B = 7.29 $ and $ L = 13.0301 $ we have:

$$ A = 7.29 + 13.0301 $$ $$ A = 7.29 + 13.0301 $$ $$ A = 20.3201 $$

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