Question

PLZ HELP QUICK!!!!!!..... Figure ABCD has vertices A(−4, 1), B(2, 1), C(2, −5), and D(−4, −3). What is the area of Figure ABCD? (1 point) 24 square units 30 square units 36 square units 45 square units

Answer 1

Answer:

The area = 30 units²

Step-by-step explanation:

∵ A (-4 , 1) and (2 , 1)

∴ AB is a horizontal segment (same y-coordinates)

∴ AB = 2 - -4 = 6 units

∵ B (2 , 1) and C (2 , -5)

∴ BC is a vertical segment (same x-coordinates)

∴ AB ⊥ BC

∴ BC = 1 - -5 = 6 units

∵ A (-4 , 1) and D (-4 , -3)

∴ AD is a vertical segment

∴ AD ⊥ AB

∴ AD // BC

∴ AD = 1 - -3 = 4 units

∴ ABCD is trapezium with parallel bases AD , BC and height AB

∵ $A=\frac{b_{1}+b_{2}}{2}h$

∴ $A=\frac{4+6}{2}(6)=30$ units²