Find the incircle radius $r$ of a hexagon if area $A = 100 cm$ .

Answer

$5.3728$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $A = 100 cm$ we have:

100 cm = \frac{3 3 \cdot a ^{2}}{2}

100 cm \cdot 2 = 33 \cdot a^{2}

200 cm = 33 \cdot a^{2}

a^{2} = \frac{200 cm}{3 3}

a^{2} = \frac{200 3}{9} cm

a = \frac{200 3}{9} cm

a \approx 6.204

STEP 2: find incircle radius $r$

To find incircle radius $r$ use formula:

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

After substituting $a = 6.204 cm^{0}$ we have:

r = \frac{3 \cdot 6.204}{2}

r = \frac{10.7457}{2}

r \approx 5.3728

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Find the incircle radius r of a hexagon if area A=100cm.

5.3728

Find the incircle radius $r$ of a hexagon if area $A = 100 cm$ .

$5.3728$