Calculate the area of the quadrilateral formed with the vertices (-3, 2), (5, 4),(7, -6) and (-5, -4).

Question

Question

This question was previously asked in

SSC CHSL 2021 (Held On : 27 May 2022 Shift 1)

Answer 1

Given:

Quadrilateral formed with the vertices (-3, 2), (5, 4),(7, -6) and (-5, -4).

Concept:

Area of quadrilateral ABCD = (1/2) ⋅ [(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) – (x₂y₁ + x₃y₂ + x₄y₃ + x₁y₄)]

Calculations:

Let A(-3, 2), B(5, 4), C(7, -6) and D(-5, -4) be the vertices of a quadrilateral ABCD.

Thus,

A(-3, 2) = (x1, y1)

B(5, 4) = (x2, y2)

C(7, -6) = (x3, y3)

D(-5, -4) = (x4, y4)

We know that,

Area of quadrilateral ABCD = (1/2) ⋅ [(x1y2 + x2y3 + x3y4 + x4y1) – (x2y1 + x3y2 + x4y3 + x1y4)]

Substituting the values,

= (). {[-3(4) + 5(-6) + 7(-4) + (-5)2] – {[5(2) + 7(4) + (-5)(-6) + (-3)(-4)]}

= ().[(-12 – 30 – 28 – 10) – (10 + 28 + 30 + 12)]

= () [-80 – 80]

= 160/2 {since area cannot be negative}

= 80

The area of the quadrilateral formed with the given vertices is 80 sq. units.