Find the long diagonal $d$ of a hexagon if incircle radius $r = 9.5 cm$ .

Answer

$21.9393 cm$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $r = 9.5 cm$ we have:

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

3 \cdot a = 9.5 cm \cdot 2

3 \cdot a = 19 cm

a = \frac{19 cm}{3}

a \approx 10.9697 cm

STEP 2: find diagonal $d$

To find diagonal $d$ use formula:

d = 2 \cdot a

After substituting $a = 10.9697 cm$ we have:

d = 2 \cdot 10.9697 cm

d \approx 21.9393 cm

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Find the long diagonal d of a hexagon if incircle radius r=9.5cm.

21.9393cm

Find the long diagonal $d$ of a hexagon if incircle radius $r = 9.5 cm$ .

$21.9393 cm$