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erik [133]
3 years ago
12

URGENT

Mathematics
1 answer:
Hunter-Best [27]3 years ago
6 0
48 because 6 multiply by 8 equals 48
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If A(-5,7), B(-4,-5), C(-1,-6) and D(4,5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.
MrMuchimi
After plotting the quadrilateral in a Cartesian plane, you can see that it is not a particular quadrilateral. Hence, you need to divide it into two triangles. Let's take ABC and ADC.

The area of a triangle with vertices known is  given by the matrix
M = \left[\begin{array}{ccc} x_{1}&y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right]

Area = 1/2· | det(M) |
        = 1/2· | x₁·y₂ - x₂·y₁ + x₂·y₃ - x₃·y₂ + x₃·y₁ - x₁·y₃ |
        = 1/2· | x₁·(y₂ - y₃) + x₂·(y₃ - y₁) + x₃·(y₁ - y₂) |

Therefore, the area of ABC will be:
A(ABC) = 1/2· | (-5)·(-5 - (-6)) + (-4)·(-6 - 7) + (-1)·(7 - (-5)) |
             = 1/2· | -5·(1) - 4·(-13) - 1·(12) |
             = 1/2 | 35 |
             = 35/2

Similarly, the area of ADC will be:
A(ABC) = 1/2· | (-5)·(5 - (-6)) + (4)·(-6 - 7) + (-1)·(7 - 5) |
             = 1/2· | -5·(11) + 4·(-13) - 1·(2) |
             = 1/2 | -109 |
<span>             = 109/2</span>

The total area of the quadrilateral will be the sum of the areas of the two triangles:

A(ABCD) = A(ABC) + A(ADC) 
               = 35/2 + 109/2
               = 72
8 0
3 years ago
In a play-school with 500 students, the number of boys is 20 more than five-sevenths of the number of girls. Let’s find the numb
Arisa [49]

Answer:

Ok, so we can express the boys as another letter. just express them as the letter B for boys.

Step-by-step explanation:

I really don't know why.

8 0
3 years ago
Round 543,982 to the nearest thousand.
Ratling [72]

Answer:

544,000

Step-by-step explanation:

6 0
3 years ago
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a hockey team ordered 12 wooden pedestals to mount their brass trophies on. The design pedestal is shown below. The teal is char
yKpoI14uk [10]

56 cause u need 12 divide by 0.08 12 times

8 0
3 years ago
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Andrea needs a box that has a volume of 90 cubic inches what might the measures of her box be
Eduardwww [97]
Volume is Length x width x height. So what are three numbers that multiply to 90?
30x30x30=90
8 0
3 years ago
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