Find the area $A$ of an equilateral triangle if circumcircle radius $R = 5 cm$ .

Answer

$\frac{75 3}{4} cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $R = 5 cm$ we have:

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

3 \cdot a = 5 cm \cdot 3

3 \cdot a = 15 cm

a = \frac{15 cm}{3}

a = 53 cm

STEP 2: find area $A$

To find area $A$ use formula:

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

After substituting $a = 53 cm$ we have:

A = \frac{3 \cdot ( 5 3 cm ) ^{2}}{4}

A = \frac{3 \cdot 75 cm ^{2}}{4}

A = \frac{75 3 cm ^{2}}{4}

A = \frac{75 3}{4} cm^{2}

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Find the area A of an equilateral triangle if circumcircle radius R=5cm.

4753​​cm2

Find the area $A$ of an equilateral triangle if circumcircle radius $R = 5 cm$ .

$\frac{75 3}{4} cm^{2}$