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.
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 $8 \mathrm{~cm}$ 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.
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not a correct explanation of Assertion (A).
Explanation:
Reason (R):
$\therefore \operatorname{ar}(\Delta \mathrm{ABC})=\frac{\sqrt{3}}{4} \times(\text { side })^{2}=\left(\frac{\sqrt{3}}{4} \times 8 \times 8\right)=16 \sqrt{3} \mathrm{~cm}^{2}$
Thus, reason (R) is true.
Assertion (A):
Area of trapezium $=\frac{1}{2} \times(25+15) \times 6=120 \mathrm{~cm}^{2}$
Thus, assertion (A) is true, but reason (R) does not give assertion (A).
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