Answer:
13 square units.
Step-by-step explanation:
We can find the area of the parallelogram using the formula:
[tex]Area=2\times \frac{1}{2}[|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|][/tex]
where [tex]A(x_1,y_1)[/tex], [tex]B(x_2,y_2)[/tex]. and [tex]C(x_3,y_3)[/tex] are the vertices of one of the triangles created by the diagonals.
[tex]Area=[|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|][/tex]
We use A(5, 3), B(8, 4), C(7, 8) to obtain:
[tex]Area=[|5(4-8)+8(8-3)+7(3-4)|][/tex]
[tex]Area=[|-20+40-7|][/tex]
[tex]Area=|13|=13[/tex]
The area of the parallelogram is 13 square units.
