CAT 2025 Lesson : Class Discussion: Geometry - Quadrilaterals: 17 to 24

Class Discussion - Quadrilaterals

Question 17

In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is
[CAT 2018 S1]

		$32\sqrt{3}$
		$24\sqrt{3}$
		$12\sqrt{3}$
		$18\sqrt{3}$

Question 18

From a rectangle ABCD of area 768 sq cm, a semicircular part with diameter AB and area 72π sq cm is removed. The perimeter of the leftover portion, in cm, is
[CAT 2018 S2]

		$80 + 16\pi$
		$82 + 24\pi$
		$86 + 8\pi$
		$88 + 12\pi$

Question 19

A parallelogram ABCD has area 48 sqcm. If the length of CD is 8 cm and that of AD is s cm, then which one of the following is necessarily true?
[CAT 2018 S2]

		$s ≠ 6$
		$s ≥ 6$
		$5 ≤ s ≤7$
		$s ≤ 6$

Question 20

Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is
[CAT 2019 S1]

		2 : 3
		5 : 6
		4 : 5
		3 : 4

Question 21

Let A and B be two regular polygons having a and b sides, respectively. If b = 2a and each interior angle of B is 3/2 times each interior angle of A, then each interior angle, in degrees, of a regular polygon with a + b sides is
[CAT 2019 S2]

Answer: 150

Question 22

A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of circle to the area of rhombus is
[CAT 2020 S1]

		$\dfrac{5\pi}{18}$
		$\dfrac{6\pi}{25}$
		$\dfrac{3\pi}{25}$
		$\dfrac{2\pi}{15}$

Question 23

The sum of the perimeters of an equilateral triangle and a rectangle is 90 cm. The area,

T

, of the triangle and the area,

R

, of the rectangle, both in sq cm, satisfy the relationship

R = T^2

. If the sides of the rectangle are in the ratio 1 : 3, then the length, in cm, of the longer side of the rectangle, is
[CAT 2020 S2]

		21
		24
		27
		18

Question 24

In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and

\angle BAD =45\degree

. If DC = 5 cm, BC = 4 cm, the area of the trapezium in sq cm is
[CAT 2020 S3]

Answer: 28

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