Mathematics
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).
Theorems on Area
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Answer
When two figures are referred to as "equal figures," it specifically means that they have the same area. It does not imply that they are congruent.
∴ Reason (R) is true.
As we know that area of a triangle = x base x height
Area of first triangle = x 8 x 6
= x 48
= 24 cm2.
Area of second triangle = x 12 x 4
= x 48
= 24 cm2.
So, area of first triangle = area of second triangle.
∴ Assertion (A) is true.
∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Hence, option 3 is the correct option.
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Related Questions
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): 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).
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).
In the figure (1) given below, ABCD is a rectangle (not drawn to scale) with side AB = 4 cm and AD = 6 cm. Find
(i) the area of parallelogram DEFC
(ii) area of △EFG.
