Find the area $A$ of a hexagon if incircle radius $r = 2 cm$ .

Answer

$83 cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $r = 2 cm$ we have:

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

3 \cdot a = 2 cm \cdot 2

3 \cdot a = 4 cm

a = \frac{4 cm}{3}

a = \frac{4 3}{3} cm

STEP 2: find area $A$

To find area $A$ use formula:

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

After substituting $a = \frac{4 3}{3} cm$ we have:

A = \frac{3 3 \cdot ( \frac{4 3}{3} cm ) ^{2}}{2}

A = \frac{3 3 \cdot \frac{16}{3} cm ^{2}}{2}

A = \frac{16 3 cm ^{2}}{2}

A = 83 cm^{2}

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Find the area A of a hexagon if incircle radius r=2cm.

83​cm2

Find the area $A$ of a hexagon if incircle radius $r = 2 cm$ .

$83 cm^{2}$