The area of the parallelogram ABCD is 90 units²
Step-by-step explanation:
Let us revise some rules
- Area of parallelogram is [tex]A=B_{1}*H_{1}=B_{2}*H_{2}[/tex]
- The line is horizontal if the y-coordinates of the points lie on it are equal
- The length of the horizontal segment whose end points are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](x_{2}-x_{1})[/tex]
- The line is vertical if the x-coordinates of the point lie on it are equal
- The length of the vertical segment whose end points are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](y_{2}-y_{1})[/tex]
Look to the attached figure
∵ ABCD is a parallelogram whose vertices are
A (-12 , 2) , B (6 , 2) , C (-2 , -3) and D (-20 , -3)
∵ The y-coordinates of points A and B are equal
∴ AB is a horizontal segment
∵ The y-coordinates of points C and D are equal
∴ CD is a horizontal segment
∴ AB // CD
∵ AB = 6 - (-12) = 6 + 12 = 18 units
∵ CD = -2 - (-20) = -2 + 20 = 18 units
∴ [tex]B_{1}[/tex] = 18 units
∵ The height of the bases AB and CD is AE
∵ AE is a vertical line
∴ The length of AE is the difference between the y-coordinates of
points A and D
∴ AE = 2 - (-3) = 2 + 3 = 5 units
∴ [tex]H_{1}[/tex] = 5 units
∵ [tex]A=B_{1}*H_{1}[/tex]
∴ A = 18 × 5 = 90 unit²
The area of the parallelogram ABCD is 90 units²
Learn more:
You can learn more about parallelograms in brainly.com/question/4459688
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