Math, asked by rakhisingh27, 5 months ago


6. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find
the area of the triangle.​

Answers

Answered by tusharraj77123
6

Answer:

Area of the isosceles triangle = 36 cm

Step-by-step explanation:

Given :

Perimeter of the isosceles triangle = 30 cm

Two equal sides are of 12 cm

To find :

Area of the triangle

Concept :

First find the third side of the isosceles triangle . So , to find the third side use this equation -:

\boxed{\sf{T=P-(12cm\times2)}}

Where,

T = Third side of the isosceles triangle

P = Perimeter

After that use this formula to find the area of the triangle.

\boxed{\sf{A=\dfrac{H\:\times\:B}{2}}}

Where,

A = Area

H = Height

B = Base

Solution :

Third side of the isosceles triangle -:

\leadsto\sf{T=30cm-(12cm\times2)}

\leadsto\sf{T=30cm-24cm}

\leadsto\sf{T=6cm}

So , the third side of the isosceles triangle is 6 cm .

Area of the isosceles triangle -:

\leadsto\sf{A=\dfrac{12cm\times6cm}{2}}

\leadsto\sf{A=\dfrac{\cancel{72}cm}{\cancel{2}}}

\leadsto\sf{A=36cm}

So , the area of the isosceles triangle is 36cm .

Answered by BlessedMess
14

First,let the third side be x.

It is given that the length of the equal sides us 12 cm and it's perimeter is 30 cm.

So,30=12+12+x

⇒ 30 = 24 + x

⇒24  + x = 30

⇒  x= 30 - 24

⇒ x = 6

So,the length of the third side is 6 cm.

Thus,the semi perimeter of the isosceles triangle (s) = 30/2 cm =15 cm

By using Heron's Formula,

Area of the triangle,

 =  \sqrt{s(s - a)(s - b)(s - c)}

 =  \sqrt{15(15 - 12)(15 - 12)(15 - 6)}  \:  {cm}^{2}

 =  \sqrt{15 \times 3 \times 3 \times 9}  \:  {cm}^{2}

 = 9 \sqrt{15}  \:  {cm}^{2}

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