Given Vertices of the Quadrilateral:
A(−4, 5),
B(0, 7),
C(5, −5),
D(−4, −2)
Step 1: Draw the quadrilateral
Plot the points A(−4,5), B(0,7), C(5,−5), and D(−4,−2) on the Cartesian plane and join them in the given order to obtain the quadrilateral ABCD.
Step 2: Use the Shoelace Formula to find the area
Arrange the coordinates cyclically:
A(−4, 5), B(0, 7), C(5, −5), D(−4, −2), A(−4, 5)
\( \text{Area} = \frac{1}{2} \left| \begin{array}{cccc} -4 & 5 \\ 0 & 7 \\ 5 & -5 \\ -4 & -2 \\ -4 & 5 \end{array} \right| \)
Step 3: Compute the products
Sum of products of xiyi+1:
(−4)(7) + (0)(−5) + (5)(−2) + (−4)(5)
= −28 + 0 − 10 − 20
= −58
Sum of products of yixi+1:
(5)(0) + (7)(5) + (−5)(−4) + (−2)(−4)
= 0 + 35 + 20 + 8
= 63
Step 4: Find the area
\( \text{Area} = \frac{1}{2} | −58 − 63 | \)
\( \text{Area} = \frac{1}{2} \times 121 = 60.5 \)
Final Answer:
The area of the quadrilateral is
60.5 square units.