Question

A trapezium PQRS is such that PQ || RS and the perpendicular from P to RS is 40 cm. If | PQ = 20 cm, |SP= 50 cm and SRI = 60 cm, calculate, correct to 2 significant figures, the area of the trapezium.​

Answer 1

Answer:

(a) Area of trapezium PQRS = 12(PQ+RS)×40

= 12(20+60)×40

= 40×40

= 1600cm2

(b) In Δ SPT,

|SP|2=|ST|2+|TP|2  (Pythagoras theorem)

|ST|2=|SP|2−|TP|2

= 502−402

= 2500−1600  

|ST|2=900

∴|ST|=30cm

|UR|=60cm−(30+20)cm

= 10 cm

Let < QRS = α,

tanα=4010=4

α=tan−1(4)

= 75.96°≊76°

Answer 2

Answer:

Area of trapezium PQRS = 12(PQ+RS)×40

= 12(20+60)×40

= 40×40

= 1600cm2

(b) In Δ SPT,

|SP|2=|ST|2+|TP|2 (Pythagoras theorem)

|ST|2=|SP|2−|TP|2

= 502−402

= 2500−1600

|ST|2=900

∴|ST|=30cm

|UR|=60cm−(30+20)cm

= 10 cm

Let < QRS = α,

tanα=4010=4

α=tan−1(4)

= 75.96°≊76°