Question

find the area of a parallelogram abcd if three of its vertices are a(2,4) b(2+√3,5) c (2,6)

Answer 1

Thank you for asking this question. Here is your answer:

If there is a diagonal in a parallelogram it bisects into two equal triangles:

which will be:

ar(llgm ABCD) = 2ar (ΔABC) -- (this will be an equation 1)

The area of triagnle with the vertices (x₁,y₁),(x₂,y₂) and (x₃,y₃)

= 1/2 [x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)]

Area of ΔABC = 1/2 [2(5-6) + (2+√3) (6-4) + 2(4-5)]

= 1/2 [-2 + 4 + 2√3-2]

= 1/2 (2√3)

= √3

so ar(llgm ABCD) = 2ar (ΔABC)

= ar(llgm ABCD) = 2 x √3  

= 2√3 is the final answer for this question.