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The isosceles triangle has perimeter = 18
base = 8 cm
so the equal sides =  (18 - 8) /2 = 5 

altitude and area are shown in the diagram...  total area = 76

area of the isosceles triangle can be also found using the formula of Heron:
  Δ = √[s (s-a) (s-b)(s-c)
  here a = 8, b = 5 c = 5      so  s = (8+5+5)/2 = 9

   Δ = area = √[ 9*1*4*4] = 12 sq cm

   Add this to the area of square = 8 * 8 = 64 cm²
  total  76 cm²

2 5 2
i am your big fan sir thanks a lot
but sir we have no altitude. so how i get area
use the formula for area of isosceles triangle ABC: one way is to find altitude using the Pythagoras theorem. so draw a perpendicular from B on to AC..
otherwise use the formula for area of triangle with 3 sides given...
answer is modified.
Area of the square= 8x8 =
area of triangle= (1/2) base x height 
Since the triangle is isosceles, the other 2 sides would be equal measuring 5cm each.
Height could be found using Pythogoras theorem[5^2- 4^2=3^2], we get height=3cm.
Area of triangle=(1/2)(3)(8)

4 is come from where
draw an imaginary perpendicular opposite to the side measuring 8cms. This would cut the triangle into half forming 2 right angled triangles. Apply Pythogoras theorem to one half and you will get the height of perpendicular which is height of the triangle. I hope this helps.
use Heron's formula..
Yes Sir, even that can be used.