Question

Assertion: The area of a trapezium whose parallel sides measure 25 cm and 15 cm respectively and the distance between them is 6 cm, is 120 cm².
Reason: The area of an equilateral triangle of side 8 cm is $16\sqrt{3}{\mathrm{cm}}^2$.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not a correct explanation of Assertion (A).

Explanation:
Reason (R):
∴ ar(∆ABC ) = $\frac{\sqrt{3}}{4}\times (\mathrm{side}{)}^2=\left(\frac{\sqrt{3}}{4}\times 8\times 8\right)=16\sqrt{3}{\mathrm{cm}}^2$
Thus, reason (R) is true.

Assertion (A):
Area of trapezium = $\frac{1}{2}\times \left(25+15\right)\times 6=120{\mathrm{cm}}^2$
Thus, assertion (A) is true, but reason (R) does not give assertion (A).