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]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%20x_%7B1%7D%26y_%7B1%7D%261%5C%5Cx_%7B2%7D%26y_%7B2%7D%261%5C%5Cx_%7B3%7D%26y_%7B3%7D%261%5Cend%7Barray%7D%5Cright%5D%20)
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
Answer:
$6.72
Step-by-step explanation:
The store is selling lemons at $0.56 each. Each lemon yields about 2 tablespoons of juice.How much will it cost to buy enough lemons to make three 9-inch lemon pies, each requiring half a cup of lemon juice?
1 cup = 16 table spoon of juice
half a cup = 8 table spoon of juice
1 pie require half a cup of lemon juice. so 1 pie requires 8 tablespoon of lemon juice
Each lemon yields about 2 tablespoons of juice
2 times 4 = 8
So 4 lemon needed to make a pie
cost of 1 lemon = 0.56
cost of 4 lemons = 
cost of lemon for making 3 pie= 
Answer:
59.8*4=239.2 rounded to the nearest foot is 239
Step-by-step explanation:
Answer:
85
Step-by-step explanation:
you will do they 20 carrots times the 4 boxes which is 80 then add the 5 her dad gave her which gives you 85
Answer:
20/18
Step-by-step explanation: