Find the incircle radius $r$ of a hexagon if area $A = 723 cm$ .

Answer

$6$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $A = 723 cm$ we have:

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

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

1443 cm = 33 \cdot a^{2}

a^{2} = \frac{144 3 cm}{3 3}

a^{2} = 48 cm

a = 48 cm

a = 43

STEP 2: find incircle radius $r$

To find incircle radius $r$ use formula:

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

After substituting $a = 43 cm^{0}$ we have:

r = \frac{3 \cdot 4 3}{2}

r = \frac{12}{2}

r = 6

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Find the incircle radius r of a hexagon if area A=723​cm.

6

Find the incircle radius $r$ of a hexagon if area $A = 723 cm$ .

$6$