If DE is a midsegment of â–ł ABC, it cuts AB and AC in two equal halves.
Note that â–ł ADE and â–ł ABC are similar triangles. This is because the ratio of two pairs of corresponding sides and their included angle are equal.
Since the triangles are similar we can use the area scale factor — which is the linear scale factor squared — to calculate the area of △ ABC.
(Linear scale factor)^2=(1/2)^2
⇓
Area scale factor=1/4
If we multiply the area of â–ł ABC with the area scale factor, we can determine the area of â–ł ADE.
96(1/4)=24 square units
