Assertion Reasoning Quiz

Assertion (A):
A circle's area can be visually proven by slicing it into tiny sectors and rearranging them to approximate a rectangle with dimensions \( \pi r \) and \( r \).
Reason (R):
The product of the base (\( \pi r \)) and height (\( r \)) of this approximated rectangle directly yields the circle's area formula, \( \pi r^2 \).

Assertion (A):
The exact area of an equilateral triangle of side \( a \) is \( \frac{\sqrt{3}}{4}a^2 \).
Reason (R):
Heron's formula can only be used for scalene triangles and fails for equilateral triangles because all sides are identical.

Assertion: A sector with central angle \(\theta\) occupies the fraction \[\frac{\theta}{360^\circ}\] of the circle’s area, and its arc has the same fraction of the circle’s circumference.
Reason: A sector is a region bounded only by an arc of a circle.

Assertion: Two parallelograms having the same pair of adjacent side lengths must have equal areas.
Reason: The area of a parallelogram is the product of a base and its corresponding perpendicular height.

Assertion: Brahmagupta’s formula is a generalisation of Heron’s formula.
Reason: Every rectangle is a cyclic quadrilateral.