Find the area $A$ of an equilateral triangle if circumcircle radius $R = 8 cm$ .

Answer

$483 cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

R = \frac{3 \cdot a}{3}

After substituting $R = 8 cm$ we have:

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

3 \cdot a = 8 cm \cdot 3

3 \cdot a = 24 cm

a = \frac{24 cm}{3}

a = 83 cm

STEP 2: find area $A$

To find area $A$ use formula:

A = \frac{3 \cdot a ^{2}}{4}

After substituting $a = 83 cm$ we have:

A = \frac{3 \cdot ( 8 3 cm ) ^{2}}{4}

A = \frac{3 \cdot 192 cm ^{2}}{4}

A = \frac{192 3 cm ^{2}}{4}

A = 483 cm^{2}

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Find the area A of an equilateral triangle if circumcircle radius R=8cm.

483​cm2

Find the area $A$ of an equilateral triangle if circumcircle radius $R = 8 cm$ .

$483 cm^{2}$