MathematicsState True/ False:If the points A(1,−2),   B 2,3 ,   C −3,2  and D(−4,−3)   are the vertices of a parallelogram ABCD, and A B as the base, then the height of the parallelogram is 24Sq.units.

State True/ False:


If the points A(1,2),   B 2,3 ,   C 3,2  and D(4,3)   are the vertices of a parallelogram ABCD, and A B as the base, then the height of the parallelogram is 24Sq.units.


  1. A
    True
  2. B
    False  

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    Solution:

    Let’s calculate the area of the parallelogram ABCD by adding the area of 2 triangles ΔABC   and ΔBCD  .
    We know, the formula of area of a triangle is,
    =12x1y2-y3+x2y3-y1+x3y1-y2, 
    Area of triangle ABC;
    ΔABC= 1 2 {1+2×4+(3)×(5)}= 1 2 (9+15)=12sq.units   Area of triangle BDC;
    ΔBCD= 1 2 {2×5+(3)×(6)+(4)}= 1 2 (10+184)=12sq.units   Thus, the area of ABCD,
    = (12+12) sq.units
    = 24Sq.units
    We have given the base of the parallelogram i.e., AB.
    Calculating the base by using the formula,
    =2-12+3+22
    =26 units
    Area of the parallelogram is 24 sq.unit.
    Thus,
    =12×base×height = 24
    = 12×AB×height = 24
    =Height = 4826units
    Therefore, the height of the parallelogram is 48 26 units  .
    Thus, the given statement is false.
    Hence, option 2 is correct.
     
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