Find b, c and d so that the quadrilateral is a parallelogram with area equal to 80 square units?

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1 Answer
Nov 7, 2016

b=14, c=8, d=18b=14,c=8,d=18

Explanation:

To achieve parallelism

y_C-y_B=y_D-y_AyCyB=yDyA

d-b= 2-(-2)db=2(2)

d=b+4d=b+4

x_C-x_B=x_D-x_AxCxB=xDxA

c-2= 4-(-2)c2=4(2)

c=2+6=8c=2+6=8

so

C=(8;b+4)C=(8;b+4)

Now let B^', D^', C^' be the projection of B,D,C on the horizontal line passing per A then

A_(ABCD) = A_(ABB^')+A_(B^'BC C^')-A_(ADD^')-A_(D^'DC C^')

so

80=(4*(b+2))/2+((b+2+b+6)*6)/2-(6*4)/2-((4+b+6)*4)/2

80=2b+4+6b+24-12-2b-20

80=6b-4

6b=84

b=14

d=18