Question

PLs, help me can't get this wrong!!!!

Answer 1

12 units squared

Step-by-step explanation:

You realize that the shape can be divided into 3 shapes;

2 right-angled triangles (one small and one bigger one) and a rectangle. We can find the area of each and then sum them up. Because we are finding area under the shape, the negative signs will be ignored;

Larger right-angled triangle;

½ b * h

½ * 4 * 4 = 8

Smaller right-angled Triangle;

½ * b * h

½ * 2 * 2 = 2

Rectangle;

L * W

2 * 1 = 2

Sum of all the areas;

2 + 2 + 8 = 12

= 12 units squared

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Answer 2

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 ( $x_{2}-x_{1}$ )

The length of a vertical segment is the difference between the y-coordinates of its endpoints ( $y_{2}-y_{1}$ )

Area of the 1st triangle

∵ The area of the right triangle = $\frac{1}{2}(leg_{1})(leg_{2})$

- The endpoints of the horizontal leg are (0 , 2) , (2 , 2)

∵ The length of $leg_{1}$ = 2 - 0 = 2 units

- The endpoints of the vertical leg are (0 ,2) , (0 , 4)

∵ The length of $leg_{1}$ = 4 - 2 = 2 units

∴ Area of the 1st triangle = $\frac{1}{2}(2)(2)$

∴ 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 $leg_{1}$ = 0 - (-4) = 0 + 4 = 4 units

- The endpoints of the vertical leg are (0 ,0) , (0 , 4)

∵ The length of $leg_{1}$ = 4 - 0 = 4 units

∴ Area of the 1st triangle = $\frac{1}{2}(4)(4)$

∴ 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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