Find the area $A$ of a hexagon if incircle radius $r = 19.5 cm$ .

Answer

$1317.2246 cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

r = \frac{3 \cdot a}{2}

After substituting $r = 19.5 cm$ we have:

19.5 cm = \frac{3 \cdot a}{2}

3 \cdot a = 19.5 cm \cdot 2

3 \cdot a = 39 cm

a = \frac{39 cm}{3}

a \approx 22.5167 cm

STEP 2: find area $A$

To find area $A$ use formula:

A = \frac{3 3 \cdot a ^{2}}{2}

After substituting $a = 22.5167 cm$ we have:

A = \frac{3 3 \cdot ( 22.5167 cm ) ^{2}}{2}

A = \frac{3 3 \cdot 507 cm ^{2}}{2}

A = \frac{2634.4493 cm ^{2}}{2}

A = 1317.2246 cm^{2}

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Find the area A of a hexagon if incircle radius r=19.5cm.

1317.2246cm2

Find the area $A$ of a hexagon if incircle radius $r = 19.5 cm$ .

$1317.2246 cm^{2}$