Find the long diagonal $d$ of a hexagon if incircle radius $r = 30.48 cm$ .

Answer

$70.3905 cm$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $r = 30.48 cm$ we have:

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

3 \cdot a = 30.48 cm \cdot 2

3 \cdot a = 60.96 cm

a = \frac{60.96 cm}{3}

a \approx 35.1953 cm

STEP 2: find diagonal $d$

To find diagonal $d$ use formula:

d = 2 \cdot a

After substituting $a = 35.1953 cm$ we have:

d = 2 \cdot 35.1953 cm

d \approx 70.3905 cm

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Find the long diagonal d of a hexagon if incircle radius r=30.48cm.

70.3905cm

Find the long diagonal $d$ of a hexagon if incircle radius $r = 30.48 cm$ .

$70.3905 cm$