The lengths of the parallel sides of a trapezium are 51 cm and 21 cm, and that of each of the other two sides is 39 cm. What is the area (in cm2) of the trapezium?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e 1296
Given that the lengths of the parallel sides of a trapezium are 51 cm and 21 cm, and that of each of the other two sides is 39 cm as shown in the figure:
In the right-angled triangle PAS
Using Pythagoras theorem:
PS2 = PA2 + AS2
⇒ AS = (PS2 - PA2)½ = (392 - 152)½ = (1296)½ = 36
Hence,
Area of the trapezium
= 0.5 × sum of parallel sides × height
= 0.5 × (PQ + SR) × AS
= 0.5 × 72 × 36
= 1296 cm2