Find the area $A$ of an equilateral triangle if incircle radius $r = 10 cm$ .

Answer

$3003 cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

r = \frac{3 \cdot a}{6}

After substituting $r = 10 cm$ we have:

10 cm = \frac{3 \cdot a}{6}

3 \cdot a = 10 cm \cdot 6

3 \cdot a = 60 cm

a = \frac{60 cm}{3}

a = 203 cm

STEP 2: find area $A$

To find area $A$ use formula:

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

After substituting $a = 203 cm$ we have:

A = \frac{3 \cdot ( 20 3 cm ) ^{2}}{4}

A = \frac{3 \cdot 1200 cm ^{2}}{4}

A = \frac{1200 3 cm ^{2}}{4}

A = 3003 cm^{2}

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Find the area A of an equilateral triangle if incircle radius r=10cm.

3003​cm2

Find the area $A$ of an equilateral triangle if incircle radius $r = 10 cm$ .

$3003 cm^{2}$