Find the area $A$ of an equilateral triangle if incircle radius $r = 17 cm$ .

Answer

$8673 cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $r = 17 cm$ we have:

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

3 \cdot a = 17 cm \cdot 6

3 \cdot a = 102 cm

a = \frac{102 cm}{3}

a = 343 cm

STEP 2: find area $A$

To find area $A$ use formula:

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

After substituting $a = 343 cm$ we have:

A = \frac{3 \cdot ( 34 3 cm ) ^{2}}{4}

A = \frac{3 \cdot 3468 cm ^{2}}{4}

A = \frac{3468 3 cm ^{2}}{4}

A = 8673 cm^{2}

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Find the area A of an equilateral triangle if incircle radius r=17cm.

8673​cm2

Find the area $A$ of an equilateral triangle if incircle radius $r = 17 cm$ .

$8673 cm^{2}$