10 seconds me area of the triangle question solve

Hello friends, maths tricks in hindi  par aapka welcome hai. Friends aapne mathematics me co-ordinate k question ko apni education life me jarur solve kiya hoga.Issi co-ordinate chapter ka ek important topic hai-: "Area of the triangle" .

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Dosto "Area of the triangle k iss topic me hum triangle k diye vertices ki help se triangle ka area find karte hai.
For example-:  Ek triangle jiska 3 vertices  (1,2),(4,3) and (1,1) hai.To Iss triangle ka area kya hoga? ya area of the triangle ko find kariye.
Note-:【vertices ko hindi me " shirsh" ( शीर्ष ) kahate hai.】


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10 seconds me area of the triangle question solve.

 Friends area of the triangle k iss type k question ko generally hum direct formula par sabhi di gayi value ko rakh kar k solve kar sakte hai.But issme time and mehanat jaada lagata hai.Sabse jada hard iss ka formula learn karna aor usko yaad rakhna hota hai.

Mai bhi issi formula ka use karunga, but thodi easy aor aashan tariko se.

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Mujhe pura bharosa hai dosto ki agar aap iss shortcut aor easy method ki 4-5 baar practice karlo to aap bhi 10 seconds me area of the triangle find kar loge.

Area of the triangle find kar fast and easy method-:

 so friends lets start karte hai , Aap iss method ko step by step follow Kare-:

#Q-1. Uss triangle ka area kya hoga ?jisk vertices A(4,6), B(3,4) and C(6,2) ho.

 Niche diye gaye step ko follow kare-:

Step-1. Diye huye 3 points (4,6),(3,4)                      and (6,2) me se sabhi k first numbers choose kare.
             (4 ,6) (3,4) ,(6,2)

Step-2. Choose kiye numbers ko niche
              jaisa likha hai , vaise likhe-:
               4(*)+3(**)+6(***)

Step-3. Diye three points k second numbers ko choose kare-:
            (4,6),(3,4),(6,2)

Step-4.

              4-2= 2...(*)
              2-6= -4...(**)
              6-4= 2...(***)
Step-5. Ab step4 se (*),(**) and (***) ki value step-2 me rakhe,solve kare aor last me 2 se divide kare.
=4×(2)+3×(-4)+6(2)
=8-12+12
=8
=8÷2
=4 Ans.



#Q-2. A(3,2) B(5,7) and C(-5,-7) 
              
Step-1. A(3,2) B(5,7) C(-5 ,-7)
Step-2.  3(*)+5(**)-5(***)
Step-3. (3,2) (5,7) (5,-7)
Step-4. 7-(-7)=14....(*)
             -7-2=-9 ....(**)
              2-7=-5 ....(***)
Step-5. (*),(**) and(***) ki value Step-2 me rakhne par-:
=3(14)+5(-9)-5(-5)
= 22
=22÷2
=11 Ans.

#Q-3. A(a,c+a) B(a,c) C(-a,c-a)
Step-1. (a,c+a) (a,c) (-a,c-a)
Step-2. a(*)+a(**)-a(***)
Step-3. (a,c+a) (a,c) (-a,c-a)
Step-4. c-(c-a)=a ....(*)
             (c-a)-(c+a)=-2a ....(**)
             (c+a)-c=a ....(***)
Step-5.
=a(a)+a(-2a)-a(a)
=-2a^2
=-2a^2÷2
=-a^2 Ans.
【-2a^2 =  "minus 2a square"】

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#Q-4. A(3,-7/2) B(7/2,-1) C(5/2,3/2)
Step-1. (3,-7/2) (7/2,-1) (5/2,3/2)
Step-2. 3(*)+7/2(**)+5/2(***)
Step-3. (3,-7/2) (7/2,-1) (5/2,3/2)
Step-4. -1-3/2=-5/2....(*)
               3/2-(-7/2)=10/2=5 ...(**)
               -7/2-(-1)=-5/2...(***)
Step-5.
=3(-5/2)+7/2(5)+5/3(-5/2)
=-15/2
=(-15/2)÷2
=15/8 Ans.

Yadi diye huye three point A,B aor C me se kisi bhi point ka first digit "0" ho , to -:

#Q-5. A(0,1) B(1,2) C(-2,-1)
Step-1. (0,1) (1,2) (-2,-1)
Step-2.  1(**)-2(***)
Step-3. (0,1) (1,2) (-2,-1)
Step-4.  -1-1=-2...(**)
               1-2=-1....(***)
Step-5.
=1(-2)-2(-1)
=-2+2
=0 Ans.


#Q-6. A(1,0) B(0,1) C(-3,-4)

Step-1. (1,0) (0,1) (-3,-4)
Step-2.  1(*)-3(***)
Step-3. (1,0) (0,1) (-3,-4)
Step-4. 1-4=-3...(*)
              0-1=-1....(***)
Step-5. 
=1(-3)-3(-1)
=0 Ans.

#Q-7.  A(0,0) B(a,0) C(0,-a)
Step-1. (0,0) (a,0) (0,-a)
Step-2. a(**)
Step-3.  (0,0) (a,0) (0,-a)
Step-4.  -a-0=-a...(**)
Step-5. 
=a(-a)
=-a^2
=-a^2÷2
-a^2/2 Ans.
#Q-8. A(0,0) B(0,2) C(2,0)
Step-1.  (0,0)(0,2)(2,0)
Step-2. 2(***)
Step-3.  (0,0) (0,2) (2,0)
Step-4. 0-2=-2 ....(***)
Step-5.
=2(-2)
=-4
=-4÷2
=-2 Ans.
#Q-9.   A(0,1) B(0,4) C(0,4)
 TRick's-:  Friends iss question ko solve karne ki jarurat hi nhi hai. Kyuki iss question k sabhi point A,B,C ka first digit "zero" hai.
Isliye isska direct hum answer"0" de sakte hai.
Friends aapko aaj ka ye 10 seconds me area of the triangle question solve karne ka easy aor fast method kaisa laga ?

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