Question

two adjacent sides of a parallelogram are 10 cm and 12 CM if its one diagonal is 4 cm long find the area of the parallelogram

Answer 1

you will have to solve for height h.
splitting the base 12 into x and 12-x where the perpendicular hits the base we get these 2 equations
h^2 + x^2 = 4^2 .... eq 1
h^2 + (12-x)^2 = 10^2 .... eq 2

eq2 - eq 1 will give
144-24x = 84
x= 60/24=2.5 cm
therefore h^2 = 16-6.25=9.75
h=
$= \sqrt{9.75}$
3.122 cm
area = 12 * 3.122 =37.464 sq cm