Find the long diagonal $d$ of a hexagon if incircle radius $r = 5 cm$ .

Answer

$\frac{20 3}{3} cm$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $r = 5 cm$ we have:

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

3 \cdot a = 5 cm \cdot 2

3 \cdot a = 10 cm

a = \frac{10 cm}{3}

a = \frac{10 3}{3} cm

STEP 2: find diagonal $d$

To find diagonal $d$ use formula:

d = 2 \cdot a

After substituting $a = \frac{10 3}{3} cm$ we have:

d = 2 \cdot \frac{10 3}{3} cm

d = \frac{20 3}{3} cm

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Find the long diagonal d of a hexagon if incircle radius r=5cm.

3203​​cm

Find the long diagonal $d$ of a hexagon if incircle radius $r = 5 cm$ .

$\frac{20 3}{3} cm$