Question:
A 2019 DSER's response:
Official solution:
Consider the overlapping triangle,
altitude = Area of quadrilateral / Side of quadrilateral
= 128/16 = 8cm
base = Side of quadrulateral/2 = 16/2 = 8cm
Then required area = Altitude x base / 2
= 8 x 8 / 2 = 32 cm^2.
留意下，
題目上每個平行四邊形，
係可以分割成4個一模一樣嘅三角形
用番平行四邊型嘅定義：
There is a midpoint W bisecting the diagonals. By drawing the midpoint to cut the side at a point X, then X also bisect the side where the overlapping triangle lies on, and WX wil be parallel to the adjacent sides. So by midpoint theorem, the overlapping triangle has the edge touching X.
The said adjacent sides are the horizontal sides of the parallelogram that parallel to line WX. You are not required to calculate the length of them, and each will NOT be equal to 8.
It is pretty wrong to assume that the triangles are equilaterial, though you can generate totally 9 overlapping triangles to form a big and similar isosceles triangle where the 2 non-horizontal lines have the length equal to 24cm each.