3420.26 – Area of a Hexagon

Let B, D, F and H be midpoints of the sides of a rectangle ACEF as shown in the figure below. Find the area of hexagon ABDEFHA given that BC = 9 and CD = 4.

3420_26_57137cb37b.png

Solution

The area of the whole rectangle ACEG is 8×18=1448 \times 18 = 144. The triangles △\triangleBCD and △\triangleFGH together form a 4 x 9 rectangle of area 36. The area of the hexagon is 144−36=108.144 - 36 = 108.