Option 1 : 12 cm^{2}

**Given:**

Sides of isosceles triangle are 5 cm, 5 cm and 8 cm.

**Concept Used:**

An isosceles triangle is a triangle that has two sides of equal length.

**Formula Used:**

Heron’s Formula → If the sides of triangle are a, b and c

And, semi Perimeter of triangle is ‘s’

Then Area of triangle = √{s(s - a)(s - b)(s - c)}

Also, Area of triangle =** **½ × base × height

**Calculation:**

Here, sides are 5 cm, 5 cm and 8 cm

⇒ Semi perimeter = s = (5 + 5 + 8)/2 = 9

⇒ area of triangle = √s(s-a)(s-b)(s-c) = √9(9 - 5)(9 - 5)(9 - 8) = √ 9 × 4 × 4 × 1 = 3 × 4 = 12 cm^{2}

By using the above information, the diagram is:

And, we know that, the height of the triangle is also the median which bisect the side BC.

Now, Δ ABD, By using Pythagoras theorem

AB^{2} = AD^{2} + BD^{2}

⇒ 5^{2} = 4^{2} + AD^{2}

⇒ AD = 3 cm

∴ Area of triangle = ½ × base × height = ½ × 8 × 3 = 12 cm^{2}