The diagram shows a quadrilateral PQRS. Given that θtan,4/3. what is the area of the quadrilateral PQRS

Answer:

16) C

Split the trapezium into a triangle and a square. Draw a perpendicular line from PS to the point Q.
Let the point on PS be A. So AQ is perpendicular to PS.

Since QR will be equal to AS, AS = 5cm
PA + AS = PS
PA = PS – AS
PA = 11 – 5 = 6cm

tanθ = ⁴⁄₃ and tanθ = AQ / PA = AQ/6

tanθ = ⁴⁄₃ = AQ / 6
²⁴⁄₃ = AQ
AQ = 8cm

AQ = RS = 8cm

Area of triangle PQA = ¹⁄₂ x PA x AQ = ¹⁄₂ x 6 x 8 = 24 cm²
Area of rectangle QRSA = QR x RS = 5 x 8 = 40 cm²

Total area = 24 + 40 = 64 cm²

OR you can use the formula for trapezium

[¹⁄₂(QR + PS) x RS] = [¹⁄₂ x (5 + 11) 8] = [16 x 4] = 64cm²