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Answer:
The area of quadrilateral ABCD is 139 unit^2.
Step-by-step explanation:
Given:
Quadrilateral ABCD whose vertices are A(1,1) B(7,-3) C(12,2) D(7,21).
Now, to find the area.
The coordinates of the quadrilateral are A(1,1), B(7,-3), C(12,2), D(7,21).
So, to find the area we need to bisect the quadrilateral ABCD and get the triangles ABC and ADC and then calculate their areas:
In Δ ABC:
Now, to get the area of triangle ABC:
On solving we get:
In Δ ADC:
Now, to get the area of triangle ADC:
On solving it by same process as above we get:
Now, to get the area of the quadrilateral we add the areas of the triangles ABC and ADC:
Therefore, area of quadrilateral ABCD is 139 unit^2.