G1.1 If an isosceles triangle has height 8 from the base, not the legs, and perimeters 32 , determine the area of the triangle.
Let the isosceles triangle be $A B C$ with $A B=A C=y$ $D$ is the midpoint of the base $B C, A D \perp B C, A D=8$ Let $B D=D C=x$
Perimeter $=2 x+2 y=32 \Rightarrow y=16-x \ldots$.
$$
x^{2}+8^{2}=y^{2}
$$
$\qquad$
Sub. (1) into (2): $x^{2}+64=256-32 x+x^{2}$
$$
x=6, y=10
$$

Area of the triangle $=48$