The lengths of the two parallel sides of a trapezium are

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The lengths of the two parallel sides of a trapezium are 28 cm and 40 cm. If the length of each of its other two sides be 12 cm, then the area (in cm2) of the trapezium is

1. 312√5
2. 408√3
3. 204√3
4. 504√3

Correct Option: C

Using Rule 9 and 1,

AE = FB = 6 cm.
In ∆ADE,
DE = √AD² - AE²
= √12² - 6²
= √(12 + 6)(12 - 6)
= √18 × 6
= 6√3cm
∴ Area of CDEF = 28 × 6√3 = 168√3 sq. cm.
Area of ∆ADE

=	1	× AE × DE
	2

=	1	× 6 × 6√3
	2

= 18√3 sq. cm.
∴ Area of trapezium = (168√3 + 2 × 18√3)sq. cm.
= 204√3 sq. cm.