The area of the following shape is 12 units²
Step-by-step explanation:
To find the are of this figure distribute it into two figures
- Right triangle with vertices (2 , 2) , (0 , 2) , (0 , 4)
- Rectangle with vertices (0 , 0) , (1 , 0) , (1 , 2) , (0 , 2)
- Right triangle with vertices (0 , 0) , (-4 , 0) , (0 , 4)
Add the area of the three figures the sum will be the area of the figure
The length of a horizontal segment is the difference between the x-coordinates of its endpoints ( [tex]x_{2}-x_{1}[/tex] )
The length of a vertical segment is the difference between the y-coordinates of its endpoints ( [tex]y_{2}-y_{1}[/tex] )
Area of the 1st triangle
∵ The area of the right triangle = [tex]\frac{1}{2}(leg_{1})(leg_{2})[/tex]
- The endpoints of the horizontal leg are (0 , 2) , (2 , 2)
∵ The length of [tex]leg_{1}[/tex] = 2 - 0 = 2 units
- The endpoints of the vertical leg are (0 ,2) , (0 , 4)
∵ The length of [tex]leg_{1}[/tex] = 4 - 2 = 2 units
∴ Area of the 1st triangle = [tex]\frac{1}{2}(2)(2)[/tex]
∴ Area of the 1st triangle = 2 units²
Area of the rectangle
∵ Area of the rectangle = l × w
∵ w = 1 - 0 = 1 units
∵ l = 2 - 0 = 2 units
∴ Area of the rectangle = 2 × 1 = 2 units²
Area of the 2nd triangle
- The endpoints of the horizontal leg are (0 , 0) , (-4 , 0)
∵ The length of [tex]leg_{1}[/tex] = 0 - (-4) = 0 + 4 = 4 units
- The endpoints of the vertical leg are (0 ,0) , (0 , 4)
∵ The length of [tex]leg_{1}[/tex] = 4 - 0 = 4 units
∴ Area of the 1st triangle = [tex]\frac{1}{2}(4)(4)[/tex]
∴ Area of the 1st triangle = 8 units²
∵ The area of the figure = area 1st Δ + area rectangle + area 2nd Δ
∴ The area of the figure = 2 + 2 + 8 = 12 units²
The area of the following shape is 12 units²
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