In the figure, PQST is a parallelogram and TSR is a straight line. If the area of \(\bigtriangleup\)QRS is 20cm2, find the area of the trapezium PQRT.
Attached Figure / Diagram
A
35cm2
B
65cm2
C
70cm2
D
140cm2
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
A\(\bigtriangleup\) = \(\frac{1}{2}\) x 8 x h = 20
= \(\frac{1}{2}\) x 8 x h = 4h
h = \(\frac{20}{4}\) = 5cm
A\(\bigtriangleup\)(PQTS) = L x H
A\(\bigtriangleup\)PQRT = A\(\bigtriangleup\)QSR + A\(\bigtriangleup\)PQTS
20 + 50 = 70cm\(^2\)
ALTERNATIVE METHOD
A\(\bigtriangleup\)PQRT = \(\frac{1}{2}\) x 5 x 28
= 70cm\(^2\)
Source: Myschool Past Questions Archive (Record #33078)