Find the long diagonal $d$ of a hexagon if area $A = 70 cm$ .

Answer

$10.3813$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $A = 70 cm$ we have:

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

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

140 cm = 33 \cdot a^{2}

a^{2} = \frac{140 cm}{3 3}

a^{2} = \frac{140 3}{9} cm

a = \frac{140 3}{9} cm

a \approx 5.1907

STEP 2: find diagonal $d$

To find diagonal $d$ use formula:

d = 2 \cdot a

After substituting $a = 5.1907 cm^{0}$ we have:

d = 2 \cdot 5.1907

d \approx 10.3813

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Find the long diagonal d of a hexagon if area A=70cm.

10.3813

Find the long diagonal $d$ of a hexagon if area $A = 70 cm$ .

$10.3813$