Answer:
Step-by-step explanation:
The attached photo shows the diagram of quadrilateral QRST with more illustrations.
Line RT divides the quadrilateral into 2 congruent triangles QRT and SRT. The sum of the angles in each triangle is 180 degrees(98 + 50 + 32)
The area of the quadrilateral = 2 × area of triangle QRT = 2 × area of triangle SRT
Using sine rule,
q/SinQ = t/SinT = r/SinR
24/sin98 = QT/sin50
QT = r = sin50 × 24.24 = 18.57
Also
24/sin98 = QR/sin32
QR = t = sin32 × 24.24 = 12.84
Let us find area of triangle QRT
Area of a triangle
= 1/2 abSinC = 1/2 rtSinQ
Area of triangle QRT
= 1/2 × 18.57 × 12.84Sin98
= 118.06
Therefore, area of quadrilateral QRST = 2 × 118.06 = 236.12
