Question

If (–1, –1), (5, –2), (6, 1) and (2, 3) taken in order are the coordinates of the vertices of a quadrilateral, then the area enclosed is,

• A. 45 sq. units
• B. 30 sq. units
• C. 22.5 sq. units
• D. 20.5 sq. units

Answer 1

The correct option is D 20.5 sq. units

Let the points be A(–1, –1), B(5, –2), C(6, 1) and D(2, 3).



$Ar\left(\Delta ABC\right)=\frac{1}{2}|-1(-2-1)+5(1+1)+6(-1+2)|$

$=\frac{1}{2}|3+10+6|=9.5\text{sq. units}$

$Ar\left(\Delta ADC\right)=\frac{1}{2}|-1(3-1)+2(1+1)+6(-1-3)|$

$=\frac{1}{2}|-2+4-24|=11\text{sq.units}$

∴ Area of quadrilateral ABCD = Ar(ΔABC) + Ar(ΔADC)

= 9.5 + 11

= 20.5 sq. units

Hence, the correct answer is option (d).