Question

The perimeter of an isosceles triangle is 32 cm. If equal side is 11cm , then the area of the triangle is?​

Answer 1

⇝GIVEN :

• Perimeter = 32cm
• Side 1 = 11cm
• Side 2 = 11cm

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⇝TO FIND :

• Area = ?

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⇝FORMULA USED :

${\red{\bigstar{\orange{\underbrace{\underline{\overbrace{\overline{\mathfrak{Area = \sqrt{s(s - a)(s - b)(s - c)} }}}}}}}}}$

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⇝SOLUTION :

❒We know that :

In an isosceles triangle 2 sides are equal and 1 side unequal.

❒First, finding the 3rd side :

${\mapsto{\bf{Perimeter = a + b + c}}}$

${\leadsto{\sf{32 = 11 + 11 + c}}}$

${\leadsto{\sf{32 = 22 + c}}}$

${\leadsto{\sf{c = 32 - 22}}}$

${\red{\underline{\bf{C = 3rd \: Side = 10cm}}}}$

❒Now, Semi-Perimeter :

${\mapsto{\bf{S = \frac{perimeter}{2} }}}$

${\leadsto{\sf{S = {\cancel\frac{32}{2} }}}}$

${\red{\underline{\bf{Semi - Perimeter = 16cm}}}}$

❒Than, Area :

${\mapsto{\bf{Area = \sqrt{s(s - a)(s - b)(s - c)} }}}$

${\leadsto{\sf{Area = \sqrt{16(16 - 11)(16 - 11)(16 - 10)} }}}$

${\leadsto{\sf{ \sqrt{16 \times 5 \times 5 \times 6} }}}$

${\leadsto{\sf{ \sqrt{2 \times 2 \times 2 \times 5 \times 1 \times 5 \times 1 \times 3 \times 2} }}}$

${\leadsto{\sf{2 \times 2 \times 5 \times 1 \times \sqrt{3} }}}$

${\large{\purple{:{\mapsto{\underline{\boxed{\bf{20 \sqrt{3} \: {cm}^{2} }}}}}}}}$

❒So,

${\red{\underline{\purple{\underline{\boxed{\pink{\mathfrak{Area = 20 \sqrt{3} {cm}^{2} }}}}}}}}$

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Answer 2

The answer = Aea is 20√6 cm².