Respuesta :
Answer:
Correct option: second one -> 21 square units
Step-by-step explanation:
First let's find the side of the square.
We can find this side finding the distance between two points of the square, using the formula:
[tex]distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Using points (1,4) and (4,7), we have:
[tex]distance = \sqrt{(1 - 4)^2 + (4 - 7)^2}[/tex]
[tex]distance = \sqrt{(-3)^2 + (-3)^2}[/tex]
[tex]distance = 3\sqrt{2}[/tex]
So the area of the square is:
[tex]area = distance^2[/tex]
[tex]area = (3\sqrt{2} )^2 = 18[/tex]
Now, let's find the three sides of the triangle:
points (5,8) and (7,8):
[tex]distance = \sqrt{(5 - 7)^2 + (8 - 8)^2} = 2[/tex]
points (7,8) and (8,5):
[tex]distance = \sqrt{(7 - 8)^2 + (8 - 5)^2} = \sqrt{10}=3.1623[/tex]
points (8,5) and (5,8):
[tex]distance = \sqrt{(8 - 5)^2 + (5 - 8)^2} = 3\sqrt{2}=4.2426[/tex]
The area of the triangle can be calculated using the formula:
[tex]area = \sqrt{p(p-a)(p-b)(p-c)}[/tex]
Where p is the semi perimeter of the triangle:
[tex]p = (a+b+c)/2 = (2+\sqrt{10} +3\sqrt{2} )/2 = 4.7025[/tex]
So the area is:
[tex]area = \sqrt{4.7025(4.7025-2)(4.7025-3.1623)(4.7025-4.2426)} = 3[/tex]
Now, adding both areas, we have:
Total area = 18 + 3 = 21 square units
Correct option: second one
