Area of PXTY is not 15 as multiplying adjacent sides to find area only works for rectangles and squares and PXTY is neither.

heres how I did it. pls correct me if I'm wrong.

we have PX = XQ = 3, PY= YR = 5 ( not explaining this since other users have explained already)

now area of PQR = 1/2 * BASE * HEIGHT = 6*8/2 = 24.
and area of PXTY = area of ▲PQR - (Area of ▲XQT + Area of ▲YTR)

consider QT = x , then TR = 8-x.

then area of ▲XQT = 1/2 * 3 * x = 3x/2 (since this is a rt. triangle length of perpendicular = height)

however ▲YTR is not right angled, so we draw a line from Y that intersects QR perpendicularly at point Z.
Now midpoint theorem states that XY || QR. since YZ is perpendicular to QR, it must also perpendicular to XY. So all angles of quadrilateral XYZQ are 90° thus XYZQ is a square. hence XQ = YZ = 3.
So area of ▲YTR = 1/2 * TR * YZ = 1/2 * (8-x) * 3 = 12 - (3x/2).

Now add area of ▲XQT + ▲YTR = [3x/2] + [12 - (3x/2)] = 12.

Area of PXTY = Area of ▲PQR - (Area of ▲XQT + ▲YTR)
= 24 - 12
= 12.

Option C is the correct answer.

It is a very easy question if you know the property that the median of a triangle divides the triangle into 2 equal halves.
As Line TX is the median, triangle PTQ have two equal area triangles: PXT and QXT.
Similarly, triangle PRT is divided into two equal are triangles: PTY and TRY.

In this way we get area of full triangle, PQR = 1/2 * PXTY

We know area of PQR = 1/2*base*height = 1/2*6*8= 24.
so PXTY = 1/2*24=12



So the correct answer is C.

Carcass how do we tell the quadrilateral is a rectangle?

Sorry, where you saw we are dealing with a rectangle ?

Carcass how do we tell PXTY is a rectangle?

Another solution using Ratios

Area of PXTY = Area of PQR - (Area of XQT + Area of YTR)
= 24 - (24 * 3/6 * QT/QR + 24 * 5/10 * TR/QR)
= 24 - 12( QT + TR )/QR
= 12

Option C

The answer is C

After finding lengths you can build a paralallogram of PXTY with base as 3 (From PX) and Height of 4 (From QT)
Area = b x h = 3x4= 12

boom!