Mathematics
Assertion (A): Area of trapezium = (sum of parallel sides) x height.
Reason (R): A parallelogram and a rectangle on the same base and between the same parallel lines are equal in area.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Theorems on Area
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Answer
By formula,
Area of trapezium = (sum of parallel sides) x height.
∴ Assertion (A) is true.
We know that,
Parallelograms on the same base and between the same parallel lines are equal in area.
A rectangle is a special type of parallelogram.
Thus, a parallelogram and a rectangle on the same base and between the same parallel lines have equal areas.
∴ Reason (R) is true.
∴ Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Hence, option 4 is the correct option.
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Related Questions
In the adjoining figure, AB || DC and AB ≠ DC. If the diagonals AC and BD of the trapezium ABCD intersect at O, then which of the following statements is not true ?
area of △ABC = area of △ABD
area of △ACD = area of △BCD
area of △OAB = area of △OCD
area of △OAD = area of △OBC
Consider the following two statements:
Statement 1: The line segment joining the mid-points of a pair of opposite sides of a parallelogram divides it into two equal parallelograms.
Statement 2: Diagonals of a parallelogram divide it into four triangles of equal area.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Assertion (A): In the adjoining figure, the two triangles are equal figures.
Reason (R): Two figures are called equal if and only if they have the same area.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Assertion (A): Two triangles having equal area are congruent.
Reason (R): Two congruent triangles have equal area.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).