Question

23. 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

Answer:

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Answer 2

The area of the quadrilateral is 28 sq units

Step-by-step explanation:

As they formed a quadrilateral when taken in order then

A = (-4,-2)

B = (-3,-5)

C = (3,-2)

D= (2,3)

in triangle ABC

area of the triangle ABC = $\frac{1}{2}[ x_1(y_2-y_3)]+ [x_2(y_3-y_1)]+{x_3(y_1-y_2)]$

area = $\frac{1}{2}$[(-4)(-5-(-2)]+(-3)(-2-(-2))+3((-2)-(-5)]

area of ABC = $\frac{1}{2}$(12+0+9) = $\frac{21}{2}$ sq unit

similarly

area of triangle ACD = $\frac{1}{2}$[(-4)((-2)-3)]+ 3(3-(-2))+ 2((-2)-(-2))

= $\frac{1}{2}$(20+15+0) = $\frac{35}{2}$ sq unit

area of the quadrilateral = area of ABC + area of ACD

= $\frac{21}{2} +\frac{35}{2}$

= 28 sq units

hence ,

The area of the quadrilateral is 28 sq units

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