*The length of the shorter altitude and the shorter side of a parallelogram are 9cm and 82 cm. The length of a longer diagonal is 15 cm. What is the area of this parallelogram?

Refer to the image attached.Given: Altitude AC = 9 cm, Diagonal AD = 15 cm, side AB = 82 cm.To find: Area of parallelogramSolution:Since, area of parallelogram = base [tex]\times[/tex] height= [tex]BD \times AC[/tex]We have to determine the base BD.Consider the triangle ABC,by Pythagoras theorem,[tex](AB)^2 = (BC)^2 + (AC)^2[/tex][tex](82)^2 = (BC)^2 + (9)^2[/tex][tex]6724-81= (BC)^2[/tex]BC = 81.5 cmNow, Consider the triangle ACD,by Pythagoras theorem,[tex](AD)^2 = (AC)^2 + (CD)^2[/tex][tex](15)^2 = (9)^2 + (CD)^2[/tex][tex]225-81= (CD)^2[/tex]CD = 12 cmNow, base BD = BC + CD= 81.5+12= 93.5 cmArea of parallelogram = BD [tex]\times AC[/tex]= 93.5 x 9= 841.5 square centimeters.Therefore, the area of parallelogram is 841.5 square centimeters.