MR-688 / 7.) problem

The heights of the parallelogram are related as 2:3, its circumference is 40 cm, and the acute angle is 30°. Calculate the area of the parallelogram.

ha:hb=2:3

3ha=2hb

hb=32ha

P=2a+b

sin 30°=hab=hba

12=hab=hba

b=2ha

a=2hb

P=22hb+2ha

P=4hb+ha

P=4ha+32ha

40=4ha+32ha

4·10=4·ha+32ha

10=ha+32ha

10=ha+32ha ·2

10·2=ha·2+32ha·2

20=2ha+3ha

20=5ha

ha=205

ha=4

hb=32·ha=32·4=32·2·2

hb=6

a=2·hb=2·6=12

A=a·ha=12·4

A=48