Question

find the area of isosceles triangle whose sides are of length 15 cm each and their side is 12 cm.​

Answer 1

✧ Given :

• sides are of length 15 cm each and their side is 12 cm.

✧ To Find :

• Area of isosceles triangle ?

✧ Solution :

• We know that,

${ \blue{ \underline{ \boxed{ \sf{ Semi - Perimeter = \frac{a + b + c}{2} }}}}}$

• Now, Substitute the values :-

$⇒{ \sf{s \: = \frac{15 + 15 + 12}{2}}}$

$⇒ \: { \sf{s = \frac{42}{2} }}$

$⇒ \: { \sf{s \: = 21 \: cm}}$

• We also know that,

${ \pink{ \underline{ \boxed{ \sf{ Area _{(triangle)} = \sqrt{s(s - a)(s - b)(s - c)} }}}}}$

• Now, Substitute the values :-

${ \sf⇒{A = \sqrt{21(21 - 15)(21 - 15)(21 - 12)}}}$

$⇒ \: { \sf{A = \sqrt{21 \times 6 \times 6 \times 9}} }$

$⇒ \: { \sf{A = 18 \sqrt{7 \times 3} }}$

$⇒ \: { \green{ \boxed{ \sf{A = 18 \sqrt{21}cm^{2} }} }}$

■ Hence, The area of isosceles triangle is 18√21 cm².

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