Question

i need an explanation

Answer 1

A triangle is always half the area of a rectangle for which it shares a side and has a third vertex on the opposite side of the rectangle.

So ADB is half the area of the square, and so is what's leftover, ADE+BDC. Since those are congruent because it's a midpoint, etc., each is one quarter the area of the square or one half the area of the middle triangle ADB.

Choice G. 1:2

Answer 2

$A_{\triangle ADE}=\dfrac{1}{2}\cdot ED \cdot AE\\\\ AE=AB\\\\ DE=\dfrac{AB}{2}\\\\A_{\triangle ADE}=\dfrac{1}{2}\cdot \dfrac{AB}{2} \cdot AB\\\\ A_{\triangle ADE}=\dfrac{(AB)^2}{4}\\\\ A_{\triangle ADB}=\dfrac{1}{2}\cdot AB\cdot AE\\\\ A_{\triangle ADB}=\dfrac{1}{2}\cdot AB\cdot AB\\\\ A_{\triangle ADB}=\dfrac{(AB)^2}{2}\\\\ \dfrac{A_{\triangle ADE}}{A_{\triangle ADB}}=\dfrac{\dfrac{(AB)^2}{4}}{\dfrac{(AB)^2}{2}}$

$\dfrac{A_{\triangle ADE}}{A_{\triangle ADB}}=\dfrac{(AB)^2}{4}\cdot\dfrac{2}{(AB)^2}=\dfrac{1}{2}=\boxed{1:2}$