Find the area of WXYZ from the figure given below provided that E, F, G, H are the respective mid points.
The correct option is AAr(WXYZ)=15Ar(ABCD) Ar[WXYZ]=15Ar[ABCD] Trapezium across the sides of the square WXYZ Note the triangle at all the 4 corners ΔAEW,ΔFXD,ΔCYG,ΔBZH Hypotenuse of each of these triangles AE, FD, GC, BH is same as the slatted sides of the trapezium. This is because E, F, G and H are midpoints ∴ AF = FD likewise for the others as well. Now by placing the triangles in such a way it coincides with the trapezium we get
Now we notice we have 5 smaller squares. Hence, areas of all the squares will be equal since they have the same side length . ∴Ar[WXYZ]=15Ar[ABCD]