Find the area $A$ of a hexagon if incircle radius $r = 9 cm$ .

Answer

$1623 cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $r = 9 cm$ we have:

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

3 \cdot a = 9 cm \cdot 2

3 \cdot a = 18 cm

a = \frac{18 cm}{3}

a = 63 cm

STEP 2: find area $A$

To find area $A$ use formula:

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

After substituting $a = 63 cm$ we have:

A = \frac{3 3 \cdot ( 6 3 cm ) ^{2}}{2}

A = \frac{3 3 \cdot 108 cm ^{2}}{2}

A = \frac{324 3 cm ^{2}}{2}

A = 1623 cm^{2}

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Find the area A of a hexagon if incircle radius r=9cm.

1623​cm2

Find the area $A$ of a hexagon if incircle radius $r = 9 cm$ .

$1623 cm^{2}$