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.

# State True/ False:If the points      and   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   and  .
We know, the formula of area of a triangle is,

Area of triangle ABC;
Area of triangle BDC;
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,
$=\sqrt{{\left(2-1\right)}^{2}+{\left(3+2\right)}^{2}}$

Area of the parallelogram is 24 sq.unit.
Thus,

Therefore, the height of the parallelogram is  .
Thus, the given statement is false.
Hence, option 2 is correct.

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