Question

Find the area $A$ of a pyramid if side $a = 19.9 cm$ and height $h = 8.2 cm$ .

Answer

$909.1715 cm^{2}$

Explanation

STEP 1: find base area $B$

To find base area $B$ use formula:

B = a^{2}

After substituting $a = 19.9 cm$ we have:

B = (19.9 cm)^{2}

B = 396.01 cm^{2}

STEP 2: find slant height $s$

To find slant height $s$ use Pythagorean Theorem:

h^{2} + \frac{a ^{2}}{4} = s^{2}

After substituting $h = 8.2 cm$ and $a = 19.9 cm$ we have:

(8.2 cm)^{2} + \frac{( 19.9 cm ) ^{2}}{4} = s^{2}

67.24 cm^{2} + \frac{396.01 cm ^{2}}{4} = s^{2}

67.24 cm^{2} + 99.0025 cm^{2} = s^{2}

s^{2} = 166.2425 cm^{2}

s = 166.2425 cm^{2}

s = 12.8935 cm

STEP 3: find lateral surface $L$

To find lateral surface $L$ use formula:

L = 2 \cdot a \cdot s

After substituting $a = 19.9 cm$ and $s = 12.8935 cm$ we have:

L = 39.8 cm \cdot 12.8935 cm

L = 513.1615 cm^{2}

STEP 4: find total surface $A$

To find total surface $A$ use formula:

A = B + L

After substituting $B = 396.01 cm^{2}$ and $L = 513.1615 cm^{2}$ we have:

A = 396.01 cm^{2} + 513.1615 cm^{2}

A = 396.01 cm^{2} + 513.1615 cm^{2}

A = 909.1715 cm^{2}

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