Find the resultant shape obtained by connecting the points where the friends arestanding (-30, -20), (-30, 5), (-20, 5) and (-20, -20). Also find the area of the figure formed.
Answers
Answer:
the shape is rectangle.
Step-by-step explanation:
let A(-30,-20) B(-30,5) C(-20,5) and D(-20,-20)
First we find all the sides by using distance formula,
AB=√(5+20)^2+(-30+30)^2
=√(25)^2+(0)^2
=√625+0
=√625
=25 unit
BC=√(5-5)^2+(-20+30)^2
=√(0)^2+(10)^2
=√0+100
=√100
=10 unit
CD=√(-20-5)^2+(-20+20)^2
=√(-25)^2+(0)^2
=√625+0
=√625
=25 unit
AD=√(-20+20)^2+(-20+30)^2
=√(0)^2+(10)^2
=√0+100
=√100
=10 unit
Now we find diagonals by using the distance formula,
AC=√(5+20)^2+(-20+30)^2
=√(25)^2+(10)^2
=√625+100
=√725
=5√29 unit
BD=√(-20-5)^2+(-20+30)^2
=√(-25)^2+(10)^2
=√625+100
=√725
=5√29 unit
Hence, when opposite sides are equal and diagonals are equal then the figure so obtained is rectangle.
For the area of figure,
we will join AC, such that we obtain triangle ACD and triangle ABC,
SO, In triangle ACD,
area=1/2[-30(5+20)+(-20)(-20+20)+(-20)(-20-5)]
=1/2[(-30×25)+(-20×0)+(-20×-25)
=1/2[(-750)+(0)+(-500)]
=1/2[-1250]
=1/2×1250
=625 sq unit
now, in triangle ABC,
area=1/2[-30(5-5)+(-30)(5+20)+(-20)(-20-5)]
=1/2[0-750+500]
=1/2[-250]
=1/2×250
=125 sq unit
so, area of figure = area of triangle ACD+ are of triangle ABC
=625+125
=750 sq unit