Question

(-4, -2), (-3, -5), (3, -2) and (2,3) are vertices Find the area of ​​the quadrilateral.
step by step please​

Answer 1

Let Vertices of quadrilateral be A(- 4, - 2), B( - 3 ,- 5), C(3 ,- 2 ) and D(2,3).

The area of a triangle is = (1/2)[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)].

Then,

Area of triangle ABC = (1/2)[-4(-5 + 2) - 3(-2 + 2) + 3(-2 + 5)]

=> (1/2)[-4(-3) - 3(0) + 3(3)]

=> (1/2)[12 + 9]

=> 21/2

Likewise,

Area of triangle ACD = (1/2)[-4(-2 - 3) + 3(3 + 2) + 2(-2 + 2)]

=> (1/2)[-4(-5) + 3(5) + 2(0)]

=> (1/2)[20 + 15]

=> 35/2

Area of quadrilateral is :

=> 21/2 + 35/2

=> 56/2

=> 28

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