Refer to the image attached.
Given: Altitude AC = 9 cm, Diagonal AD = 15 cm, side AB = 82 cm.
To find: Area of parallelogram
Solution:
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 cm
Now, 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 cm
Now, base BD = BC + CD
= 81.5+12
= 93.5 cm
Area 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.
