പാദം 4 cm ആയ ഒരു സമപാർശ്വ ത്രികോണത്തിന്റെ തുല്യവശങ്ങൾ 6 cm വീതം ആയാൽ അതിന്റെ പരപ്പളവ് എത്രയായിരിക്കും?

We are given an isosceles triangle with a base of 4 cm and the two equal sides (legs) each measuring 6 cm.

1. Finding the height:
   Since the triangle is isosceles, the height (h) divides the triangle into two right triangles, each with a base of 2 cm (half of the 4 cm base).

   Using the Pythagorean theorem:

   $$h^2 + 2^2 = 6^2$$ $$h^2 + 4 = 36$$ $$h^2 = 36 - 4 = 32$$ $$h = \sqrt{32} = 4\sqrt{2} \, \text{cm}$$

2. Calculating the area:
   The area $A$ of a triangle is given by the formula:

   $$A = \frac{1}{2} \times \text{base} \times \text{height}$$

   Substituting the values:

   $$A = \frac{1}{2} \times 4 \times 4\sqrt{2} = 8\sqrt{2} \, \text{cm}^2$$

Answer:
(A) 8√2 cm²