Question

find the area of an Isosces triangle whose perimeter is 32 cm and base is 12 cm​

Answer 1

• Answer :- Area of the isosceles triangle is 48 m².
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Answer 2

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$\huge\bold\pink{Solution:-}$

★ Answer:-

⛄ Area of the given isosceles triangle= 48 cm²

★ Step-by-step explanation:-

We know that an isosceles triangle has two equal sides.

Now, let the two unknown equal sides be considered as 2x.

We are also given that the base of the iso. triangle measures 12 cm and it's perimeter is 32 cm.

Therefore, here goes the equation:-

12 + 2x = 32

=> 2x = 32 - 12

=> 2x = 20

=> x = 10 cm.

Now, to find the semi perimeter of the triangle, we have the formula;

s = a + b + c/2

where a, b, c are the sides of the triangle.

On substituting the given values on the formula, we get,

s = 12 + 10 + 10 / 2

=> s = 32/2

=> s = 16 cm.

Area of the triangle using Heron's formula =

√s (s - a) (s - b) (s - c)

=> √16 (16 - 12) (16 -10) (16 -10) cm²

=> √16 (4) (6) (6) cm²

=> 6 √64 cm²

=> 6 × 8 cm²

=> 48 cm²

[Required area of the isosceles triangle]

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