Four friends Ram, Mohan, Ajay and Sanjay are playing in a rectangular playground. Ram suggested his friends to get the position by keeping a stone in the middle of the park and he told the stone is the origin for their position. Now, they got the position of all four friends as (– 4, – 2), (– 3, – 5), (3, – 2) and (2, 3). Mohan claimed that their position will form a quadrilateral if taken in order. Ajay and Sanjay are now trying to calculate the area of the quadrilateral formed by their position if taken in order. How much area they calculated.
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The area will be 28 sq units
- We know that when four vertices are provided, the area of the quadrilateral is deined by the formula
A = (1/2) * { (x₁y₂+x₂y₃+x₃y₄+x₄y₁) - (x₂y₁+x₃y₂+x₄y₃+x₁y₄) }
- Given points - (– 4, – 2), (– 3, – 5), (3, – 2) and (2, 3)
- putting the points in the equation,
A = (1/2) * { (-4*-5 + -3*-2 + 3*3 + 2*-2) - (-2*-3 + 3*-5 + 2*-2 + -4*3) }
= (1/2) * { (20 + 6 + 9 -4) - (6 - 15 - 4 - 12) }
= (1/2) * { 31 + 25 }
= 0.5 * 56 = 28 sq units
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