Find the area $A$ of a hexagon if incircle radius $r = 5.8 cm$ .

Answer

$116.5324 cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $r = 5.8 cm$ we have:

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

3 \cdot a = 5.8 cm \cdot 2

3 \cdot a = 11.6 cm

a = \frac{11.6 cm}{3}

a \approx 6.6973 cm

STEP 2: find area $A$

To find area $A$ use formula:

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

After substituting $a = 6.6973 cm$ we have:

A = \frac{3 3 \cdot ( 6.6973 cm ) ^{2}}{2}

A = \frac{3 3 \cdot 44.8533 cm ^{2}}{2}

A = \frac{233.0648 cm ^{2}}{2}

A = 116.5324 cm^{2}

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Find the area A of a hexagon if incircle radius r=5.8cm.

116.5324cm2

Find the area $A$ of a hexagon if incircle radius $r = 5.8 cm$ .

$116.5324 cm^{2}$