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Class Discussion: Geometry

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CAT 2025 Lesson : Class Discussion: Geometry - Quadrilaterals: 9 to 16

Class Discussion - Quadrilaterals

Question 9

In a quadrilateral ABCD, BC = 10, CD = 14, AD = 12 and

\angle

CBA =

\angle

BAD = 60°. If AB =

a + \sqrt{b}

, where

a

and

b

are positive integers then

a + b =

[XAT 2009]

		193
		201
		204
		207
		None of the above

Question 10

Let

S_{1}, S{2}, ...

be the squares such that for each

n \geq 1

, the length of the diagonal of

S_{n}

is equal to the length of the side of

S_{n+1}

. If the length of the side of

S_{3}

is 4 cm, what is the length of the side of

S_{n}

?
[XAT 2010]

		$2^{(\frac{2n + 1}{2})}$
		$2(n - 1)$
		$2^{(n - 1)}$
		$2^{(\frac{n + 1}{2})}$
		None of the above

Question 11

The figure below has been obtained by folding a rectangle. The total area of the figure (as visible) is 144 square meters. Had the rectangle not been folded, the current overlapping part would have been a square. What would have been the total area of the original unfolded rectangle (in m

^{2}

[XAT 2015]

		128
		154
		162
		172
		None of the above

Question 12

The parallel sides of a trapezoid ABCD are in the ratio of 4 : 5. ABCD is divided into an isosceles triangle ABP and a parallelogram PBCD (as shown below). ABCD has a perimeter equal to 1120 meters and PBCD has a perimeter equal to 1000 meters. Find Sin

\angle

ABC, given 2

\angle

DAB =

\angle

BCD.

[XAT 2015]

		$\dfrac{4}{5}$
		$\dfrac{16}{25}$
		$\dfrac{5}{6}$
		$\dfrac{24}{25}$
		A single solution is not possible

Question 13

If the diagonals of a rhombus of side 15 cm are in the ratio 3 : 4, find the area of the rhombus.
[XAT 2018]

		54 sq. cm.
		108 sq. cm.
		144 sq. cm.
		200 sq. cm.
		None of the above

Question 14

In the picture below, EFGH, ABCD are squares, and ABE, BCF, CDG, DAH are equilateral triangles. What is the ratio of the area of the square EFGH to that of ABCD?

[XAT 2019]

		$\sqrt{3} + 2$
		$\sqrt{2} + \sqrt{3}$
		$\sqrt{2} + 2$
		200 sq. cm.
		None of the above

Question 15

Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is
[CAT 2017 S2]

		$3\sqrt{2}$
		$3$
		$4$
		$\sqrt{3}$

Question 16

Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is
[CAT 2018 S1]

		4 : 9
		1 : 3
		2 : 5
		3 : 8

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