PQRS is a trapezium in which |PS| = 9cm, |QR| = 15cm, |PQ| = \(2\sqrt{3}, \angle PQR = 90^o and \angle QRS = 30^o\). Calculate the area of the trapezium
Attached Figure / Diagram
A
\(24\sqrt{3} cm^2\)
B
\(36\sqrt{3} cm^2\)
C
\(42\sqrt{3} cm^2\)
D
\(72\sqrt{3} cm^2\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Area of trapezium = \(\frac{1}{2}\)( a + b) x h
a = 9cm, b = 15cm, c = (15 - 9) = 6cm since height was not given, so we calculate for it using trig . ratio
h = 2\(\sqrt{3}\)cm
Area of trapezium = \(\frac{1}{2}\)( a + b ) x h = \(\frac{1}{2}\)( 9 + 15 ) x 2\(\sqrt{3}\)
= 24 x \(\sqrt{3}\) = 24\(\sqrt{3}\)cm\(^2\)
Source: Myschool Past Questions Archive (Record #26520)