The lengths of the parallel sides of the 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.
We need to find the height of the area of the trapezium to find its area, which we can find by Pythagoras theorem as the parallel part of the longer side will be equal to the shorter part opposite to it when a perpendicular will be drawn as the height of the trapezium.
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 a right-angled triangle PAS,
Using Pythagoras theorem
(PS)2 = (PA)2 + (AS)2
(39)2 = (15)2 + (AS)2
AS = √(1521 - 225) = √1296 = 36 cm
Area of the trapezium = 1/2(Sum of parallel sides) × Height
= 1/2 × (72) × 36 = 1296 cm2