In the figure below, $ABDC,$ $EFHG,$ and $ASHY$ are all squares; $AB=EF =1$ and $AY=5$.
What is the area of quadrilateral $DYES$?
+128475 The area of the two small squares combined is 2 units^2
Note that CY = AY - AC = AY - AB = 5 - 1 = 4
And CD = AB = 1
So...the area of triangle CDY = (1/2) CY * CD = (1/2) (4) ( 1) = 2 units^2
And, by symmetry, triangles BDS , YEG and SEF will have the same area as triangle CDY
So...the area of quadrilateral DYES =
Area of square ASHY less areas of the two smaller squares less areas of the four triangles =
5^2 - 2 - 4 (2) =
25 - 2 - 8 =
25 - 10 =
15 units^2
