The area of ABCD is calculated as: 25 square units.
Given the following vertices for ABCD as:
A (5,-5),
B(8,5),
C(11, -15),
D(8, – 15)
The area of ABCD = area of triangle ABC + area of triangle ADC.
Use the area of a triangle formula, 1/2|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|, to find the area of triangle ABC and the area of triangle ADC.
Area of triangle ABC:
A (5,-5) = (x1, y1)
B(8,5) = (x2, y2)
C(11, -15) = (x3, y3)
Plug in the values
Area of triangle ABC = 1/2|5(5 - (-15)) + 8(-15 - (-5)) + 11(-5 - 5)|
Area of triangle ABC = 1/2|100 - 10 - 110|
Area of triangle ABC = 1/2|-20|
Area of triangle ABC = 10 units²
Area of triangle ADC:
A (5,-5) = (x1, y1)
D(8, – 15) = (x2, y2)
C(11, -15) = (x3, y3)
Plug in the values
Area of triangle ADC = 1/2|5(-15 - (-15)) + 8(-15 - (-5)) + 11(-5 - (-15))|
Area of triangle ADC = 1/2|0 - 80 + 110|
Area of triangle ADC = 1/2|30|
Area of triangle ADC = 15 units²
Area of ABCD = 10 + 15 = 25 units².
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