Question

find the area of an isosceles triangle having the base x cm and oneside y cm

Answer 1

The area of an isosceles triangle is = 1/2 * base * height .
Here we know the base = x 
Now we need to find the height .
For that join the top corner of the triangle to the mid point of the base . Name the top corner as b and the mid point of the base as c.
Now as two triangles are formed consider any one triangle .
Both the triangles are right angled .
So by Pythagoras theorem we have
Height^2+1/2Base^2=y^2
Height^2+1/2x^2=y^2
Height^2=y^2-1/2x^2
height = y-1/4x

So the area = 1/2 * base * height = 1/2 * x * (y-1/4x)
=1/2x(4y-x /  4)   (solving inside the bracket)
=4xy-x^2 / 8