Question

Find the area of the quadrilateral the coordinates of whose angular points
taken in order are (1, 1), (3, 4), (5,-2), and (4, -7).​

Answer 1

Answer:

Lets name A (1,1)______________B (3,4 )

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D (4,-7) C (5,-2)

Rough Figure

Area using the triangle formula

ABCD = Triangle ABC + Triangle ACD

Triangle ACD =1/2{ x1(y2-y3) + x2(y3-y1) +x3(y1-y2)}

= 1/2{ 1(-2-(-7)) + 5(-7-1) +4(1-(-2))}

= 1/2{ 5 -40 +12}

= 1/2{-23} = -23/2 = -11.5 = 11.5 because the value of triangle can't be negative

Triangle ABC =1/2{ 1(4+2) + 3(-2-1) + 5(1-4 )

= 1/2{ 6 -6 +-15}

= 1/2(-15) = -7.5 = 7.5

Total area of ABCD =11.5 + 7.5 = 19 unit square