Question

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.

Answer 1

The are is 28

Explanation:

Given:

Point 1: (– 4, – 2)

Point 2: (– 3, – 5)

Point 3: (3, – 2)

Point 4: (2, 3)

then, the coordinates of the first point are x1 = -4, y1 = -2; of the second point x2 = -3, y2 = -5; and so on.

We can compute the area of the quadrilateral with the shoelace formula as follows:

area = 1/2 * |x1*y2 + x2*y3 + x3*y4 + x4*y1 - x2*y1 - x3*y2 - x4*y3 - x1*y4 |

area = 1/2 * |(-4)*(-5) + (-3)*(-2) + 3*3 + 2*(-2) - (-3)*(-2) - 3*(-5) - 2*(-2) - (-4)*3 |

area = 1/2 * 56 = 28

Answer 2

The area calculated by them is 21.

Explanation:

The given points are (-4,-2),(-3,-5),(3,-2) and (2,3).

The area of the quadrilateral:

A=
`((x1 y2+x2y3+x3y4+x4y1)-(x2y1+x3y2+x4y3+x1y4) )/(2)`.

From the given points,

A=
`((20+6+9-4)-(6-1-4-12) )/(2)`

A=
`((31)-(-11) )/(2)`

A=
`(42)/(2)`

The area of the quadrilateral = 21.