Question stem:- What is the area of the quadrilateral KMNL?

St1:- x = y = 45

Refer the enclosed diagram, \(\triangle{NQL}\), \(\triangle{KPO}\), and \(\triangle{KMP}\) are isosceles right angled triangles(45-45-90) form. sides are in the ratio \(x:x:\sqrt{2}x\)
So base=height=10 and hypotenuse=\(10\sqrt{2}\)

Hence area of \(\triangle{NQL}\)=Area of \(\triangle{KPO}\)=Area of \(\triangle{KMP}\) (Base and height are known, area can be determined)

Total area of figure=Area of shaded region(100)+3*Area of triangle NQL
Sufficient.

St-2:- QL = 10
Area of the figure will be different at different measures of x.
Insufficient.

Ans. (D)


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Regards,

PKN

Rise above the storm, you will find the sunshine

Hi gvij2017,

1. Shaded region is square.- we needn't to know the type of quadrilateral it is. We have to find the area of the triangles, add the area of shaded region to get the area of total figure.
2. KL is parallel to MN:- a) KM is perpendicular to MN b)PO perpendicular to KL c) NQ perpendicular to KL ,Hence KL || MN

NO ASSUMPTIONS WERE MADE.
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Regards,

PKN

Rise above the storm, you will find the sunshine

Hi funsogu,
You have pointed it out correctly. My bad ,how did I write D? It is A. Need to fix typo error.

Posted from my mobile device
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine