Q32 of 83 Page 356

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct answer.











Assertion (A)



Reason (R)



In the given figure, ABCD is a ‖ gm in which DE ⊥ AB and BF ⊥ AD. If AB = 16cm, DE = 8cm and BF = 10cm, then AD is 12cm.




Area of a ‖gm = base x height.


Here, let AB be the base of the parallelogram then DE becomes its altitude (height).


Area of the parallelogram is given by: Base × Height


∴ Area of ‖gm ABCD = AB×DE = 16×8 = 128cm2


Now,


Consider AD as base of the parallelogram then BF becomes its altitude (height)


∴ area of ‖gm ABCD = AD × BF = 128cm2


AD × 10 = 128cm2


AD = = 12.8cm


∴length of AD = 12.8cm


∴Assertion is false and Reason is true

More from this chapter

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30

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct answer.











Assertion (A)



Reason (R)



The diagonals of a ‖ gm divide it into four triangles of equal area.



A diagonal of a ‖ gm divides it into two triangles of equal area.


 31

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct answer.











Assertion (A)



Reason (R)



The area of a trapezium whose parallel sides measure 25cm and 15cm respectively and the distance between them is 6cm, is 120cm2.



The area of an equilateral triangle of side 8cm is 163cm2.


 33

Which of the following is a false statement?

(A) A median of a triangle divides it into two triangles of equal areas.


(B) The diagonals of a ‖gm divide it into four triangles of equal areas.


(C) In a ∆ABC, if E is the midpoint of median AD, then ar(∆BED) = ar(∆ABC).



(D) In a trap. ABCD, it is given that AB‖DC and the diagonals AC and BD intersect at O. Then, ar(∆AOB) = ar(∆COD).


 34

Which of the following is a false statement?

A) If the diagonals of a rhombus are 18cm and 14cm, then its area is 126cm2.


B) Area of a ‖gm = x base x corresponding height.


C) A parallelogram and a rectangle on the same base and between the same parallels are equal in area.


D) If the area of a ‖ gm with one side 24cm and corresponding height h cm is 192cm2, then h = 8cm.