Here the side length a=8(cm) and the area of rhombus S=36(cm^2) are known values, but the height of altitude h is the unknown which we are to find relating to a and S. Label each vertex of the rhombus A,B,C and D, respectively, counterclockwise from an acute vertex. Draw a line connecting B and D, and an altitude from D to the foot H on side AB. The altitude DH intersects side AB perpendicularly at H. Therfore, the area of triangle ABD is s=1/2(side ABx altitude BD)=ah/2. While triangle ABD is congruent to triangle BCD since each side of a rhombus is congruent to each other, and both triangles share side BD. (S.S.S) Therfore, S=2xs=2xah/2=ah. This equation S=ah expesses: The area of a rhombus=(the side)x(the altitude). Plug S=36(cm^2) and a=8(cm) into the equation obtained above. 36=8xh, h=36/8=4.5 CK: 4.5(cm)x8(cm)=36(cm^2) The altitude of the rhombus is 4.5cm.
