Question

find the area of a quadrilateral region formedby the point (1,1) (3,4) (5-2) (4,7)




step by step ​

Answer 1

Step-by-step explanation:

supposed first number is equal to x

Answer 2

Let the points be A (1, 1), B (3, 4), C (5, –2) and D (4, –7)

Plot the points we get the quadrilateral as shown

Divide the quadrilateral in two triangles by joining points A and C thus by observing figure we can conclude that

area(ABCD) = area(ΔABC) + area(ΔACD)

let us find area(ΔABC)

vertices are

A = (x1, y1) = (1, 1)

B = (x2, y2) = (3, 4)

C = (x3, y3) = (5, -2)

Area of triangle is given by formula

Area =

× [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]

Where (x1, y1), (x2, y2) and (x3, y3) are vertices of triangle

Substituting values

⇒ area(ΔABC) =

× [1(4 – (-2)) + 3(-2 – 1) + 5(1 – 4)]

⇒ area(ΔABC) =

× [6 + (-9) + (-15)]

⇒ area(ΔABC) =

× [6 - 24]

⇒ area(ΔABC) = -9

As area cannot be negative

⇒ area(ΔABC) = 9 unit2

Let us find area(ΔACD)

Vertices are

A = (x1, y1) = (1, 1)

C = (x2, y2) = (5, -2)

D = (x3, y3) = (4, -7)

⇒ area(ΔACD) =

× [1(-2 – (-7)) + 5(-7 – 1) + 4(1 – (-2))]

⇒ area(ΔACD) =

× [5 + (-40) + 12]

⇒ area(ΔACD) =

× [-40 + 17]

⇒ area(ΔACD) = 11.5 unit2

Thus, area(ABCD) = area(ΔABC) + area(ΔACD)

⇒ area(ABCD) = 9 + 11.5

⇒ area(ABCD) = 20.5 unit2

Therefore, area of quadrilateral region is 20.5 unit2

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