Find the area of quadrilateral ABCD whose vertices are A(-3,-1), B(-2,-4), C(4,-1), and D(3,4).

Concept- We'll plot the points and connect the vertices with their neighboring vertices to begin answering this question. We shall then join the diagonal AC after that. Then, we will have two triangles, and the area of the quadrilateral ABCD will be equal to the sum of the areas of those two triangles.
The area of the quadrilateral ABCD shown in the previous figure has to be determined.
Given that a quadrilateral's vertices are A(-3, -1), B(-2, -4), C(4, -1), and D (3,4).
Now, what we'll do is draw a straight line connecting points A and C that is diagonal to the quadrilateral ABCD.
Two triangles, triangle ABC and triangle ADC with base AC, are seen in the figure.
We now understand that the area of a triangle whose three vertices are A (a, b), B (c, d), and C (e, f) is equal to,The vertices of triangle ABC are A (-3, -1), B (-2, -4), and C. ( 4, -1 ).
So, area of triangle ABC will be= When we simplify, we obtain:
The vertices of triangle ADC are A (-3, -1), D (3, 4), and C. ( 4, -1 ).
So, area of triangle ADC will be=on simplifying, we get
Due to the fact that area cannot be negative, the triangle's area is .
Figure shows that the area of the quadrilateral ABCD is the sum of the areas of the triangles ABC and ADC.
Area of the quadrilateral ABCD is thus equal to After solving, we see that the quadrilateral's area is .
Hence,the correct option is 1) 28.