# 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.

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 $8 \mathrm{~cm}$ 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.

Solution:

(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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