\(A(-2,\,-1)\), \(B(4,\,-3)\), \(C(5,\,2)\) and \(D(0,\,5)\) are the vertices of a quadrilateral ABCD, taken in order. What is the area of the quadrilateral?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 34 square units
The diagonal AC splits the quadrilateral into two triangles, ABC and ACD; their areas, from \(\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|\), are added.
Triangle ABC: \(-2(-3-2)+4(2-(-1))+5(-1-(-3))=10+12+10=32\)
Area of ABC \(\displaystyle =\frac{1}{2}\times32=16\) square units
Triangle ACD: \(-2(2-5)+5(5-(-1))+0(-1-2)=6+30+0=36\)
Area of ACD \(\displaystyle =\frac{1}{2}\times36=18\) square units
Area of ABCD \(=16+18=34\) square units
