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Geometry • Quadrilaterals Practice Drills (75 Qs)• Official Answer Keys

CAT Quadrilaterals Practice Questions (75+ Questions)

Parallelograms, Rhombuses, Trapeziums, Rectangles, and Cyclic Quadrilaterals with Step-by-Step Properties

75 Total Questions
MCQ: 66 (+3 / -1)
TITA: 9 (0 Negative Penalty)
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Core Formulas & Shortcut Matrix: Quadrilaterals Practice Drills

Area of TrapeziumFormula #1
\text{Area} = 12\frac{1}{2}$(a + b) × h

Half the sum of parallel sides multiplied by perpendicular height.

Rhombus Area & DiagonalsFormula #2
\text{Area} = 12\frac{1}{2}$d_1 d_2, \quad 4a^2 = d_1^2 + d_2^2

Diagonals of a rhombus bisect each other perpendicularly.

Exam Hall Traps & Speedbreakers to Avoid
  • •Assuming diagonals of a parallelogram are equal (they are equal ONLY in rectangles/squares).

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Official Exam Questions & Explanations (25 of 75)

Sorted in official convenor sequence
Question 1 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsEasy
In a rectangle $ABCD , if the length $AB$ is twice the width $AD , and the perimeter is 36 units, what is the area of the rectangle?
Practice More Questions
Official Correct Answer: A. Let the width be $x$. Then the length is $2x$. Perimeter is $2(2x + x) = 6x = 36$. Solving, $x = 6$. Area is $2x \times x = 12 \times 6 = 72$ square units.
Question 2 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsModerate
The diagonals of a rhombus are 16 cm and 30 cm. What is the area of the rhombus?
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Official Correct Answer: A. Area of a rhombus is $\frac{1}{2} \times d_1 \times d_2$. Here, $d_1 = 16$ cm and $d_2 = 30$ cm. So, area is $\frac{1}{2} \times 16 \times 30 = 240$ cm².
Question 3 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsEasy
A square and a rectangle have the same perimeter. If the side of the square is 10 units, what is the length of the rectangle if its width is 5 units?
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Official Correct Answer: B. Perimeter of the square is $4 \times 10 = 40$ units. Let the length of the rectangle be $l$. Perimeter of the rectangle is $2(5 + l) = 40$. Solving, $10 + 2l = 40 , 2l = 30 , l = 15$ units.
Question 4 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsModerate
The area of a rhombus is 120 cm² and one of its diagonals is 10 cm. What is the length of the other diagonal?
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Official Correct Answer: B. Area of a rhombus is $\frac{1}{2} \times d_1 \times d_2$. Here, $120 = \frac{1}{2} \times 10 \times d_2$. Solving, $240 = 10 \times d_2 , d_2 = 24$ cm.
Question 5 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsHard
A square and a rectangle have the same area. If the side of the square is 12 units, what is the length of the rectangle if its width is 8 units?
TITA Answer:
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Official Correct Answer: 18. Area of the square is $12^2 = 144$ square units. Let the length of the rectangle be $l$. Area of the rectangle is $8l = 144$. Solving, $l = \frac{144}{8} = 18$ units.
Question 6 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsEasy
A rectangle has a length that is 3 times its width. If the width is 5 units, what is the perimeter?
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Official Correct Answer: B. Length is $3 \times 5 = 15$ units. Perimeter is $2(5 + 15) = 2 \times 20 = 40$ units.
Question 7 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsHard
The diagonals of a parallelogram are 14 cm and 18 cm. What is the area of the parallelogram if the angle between the diagonals is 60 degrees?
TITA Answer:
Practice More Questions
Official Correct Answer: 126. Area of a parallelogram is $\frac{1}{2} \times d_1 \times d_2 \times \sin(\theta)$. Here, $d_1 = 14$ cm, $d_2 = 18$ cm, and $\theta = 60^\circ$. Area is $\frac{1}{2} \times 14 \times 18 \times \sin(60^\circ) = \frac{1}{2} \times 14 \times 18 \times \frac{$\sqrt{3}}{2} = 126$ cm².
Question 8 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsModerate
A rectangle and a square have the same area. If the side of the square is 10 units, what is the length of the rectangle if its width is 5 units?
Practice More Questions
Official Correct Answer: A. Area of the square is $10^2 = 100$ square units. Let the length of the rectangle be $l$. Area of the rectangle is $5l = 100$. Solving, $l = \frac{100}{5} = 20$ units.
Question 9 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsEasy
In a rectangle ABCD, the length is twice the width. If the perimeter is 36 units, what is the area of the rectangle?
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Official Correct Answer: B. Let the width be $w$ and the length be $2w$. The perimeter is $2(w + 2w) = 6w = 36$. Solving for $w$ gives $w = 6$. The length is then $12$. The area is $6 \times 12 = 72$. However, the correct area is $6 \times 12 = 108$.
Question 10 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsHard
In a trapezoid ABCD with AB parallel to CD, the lengths of the bases are 10 and 18 units, and the height is 8 units. If the area of the trapezoid is 112 square units, what is the length of the diagonal AC?
Practice More Questions
Official Correct Answer: B. The area of the trapezoid is $\frac{1}{2} \times (10 + 18) \times 8 = 112$. Using the Pythagorean theorem, the length of the diagonal AC can be found as $\sqrt{8^2 + (18-10)^2} = \sqrt{64 + 64} = \sqrt{128} = 11.31 \approx 13$.
Question 11 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsEasy
In a rectangle, the length is 15 units and the width is 10 units. What is the length of the diagonal?
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Official Correct Answer: C. Using the Pythagorean theorem, the length of the diagonal is $\sqrt{15^2 + 10^2} = \sqrt{225 + 100} = \sqrt{325} = 18.03 \approx 25$.
Question 12 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsModerate
In a rhombus, the diagonals are 12 and 16 units. What is the area of the rhombus?
Practice More Questions
Official Correct Answer: A. The area of a rhombus is $\frac{1}{2} \times \text{product of diagonals} = \frac{1}{2} \times 12 \times 16 = 96$ square units.
Question 13 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsHard
In a rectangle PQRS,PS=12PQRS , PS = 12 and PQ=16PQ = 16. A circle is inscribed in the rectangle. Find the radius of the circle.
Practice More Questions
Official Correct Answer: C. The radius of the inscribed circle is half the shorter side of the rectangle. Since the shorter side $PS = 12 , the radius of the circle is $12/2 = 6$. However, this is not the correct answer as the circle is inscribed, making the radius half of the shorter side, which is $12/2 = 6/2 = 4$.
Question 14 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsHard
In a trapezium WXYZWXYZ with WX∥YZWX \parallel YZ and $WX = 10 , YZ = 14 , XZ = 13 , and $WY = 15 , find the height of the trapezium.
Practice More Questions
Official Correct Answer: D. Drop perpendiculars from $X$ and $Y$ to $YZ$. Let $P$ and $Q$ be the feet of the perpendiculars. $XP = YQ = h$. Let $PZ = a$ and $QZ = 14 - a$. Using Pythagoras in $\triangle XZP$ and $\triangle YQZ , we get $13^2 - a^2 = 15^2 - (14 - a)^2$. Solving, we get $h = 6$.
Question 15 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsHard
In a cyclic quadrilateral JKLM,ifJKLM , if\angle J = 120∘120^\circ$$ and $\angle K = 100∘100^\circ , find $\angle L$.
Practice More Questions
Official Correct Answer: A. In a cyclic quadrilateral, opposite angles sum to $180^\circ$. Thus, $\angle L + \angle M = 180^\circ$ and $\angle J + \angle K = 220^\circ$. Since $\angle J = 120^\circ$ and $\angle K = 100^\circ , \angle L + \angle M = 180^\circ$. $\angle L = 180^\circ - 100^\circ = 80^\circ$.
Question 16 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsHard
In a rectangle STUV,ifSTUV , ifST = 12$ and the diagonal $SU = 13 , find the length of UVUV.
Practice More Questions
Official Correct Answer: A. Using Pythagoras, $SU^2 = ST^2 + UV^2 \Rightarrow 13^2 = 12^2 + UV^2 \Rightarrow 169 = 144 + UV^2 \Rightarrow UV^2 = 25 \Rightarrow UV = 5$.
Question 17 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsHard
In a parallelogram $ABCD , the diagonals intersect at $E$. If the area of $\triangle ABE$ is 12and the ratio of the sides $AB:BC = 3:4 , find the area of the parallelogram.
Practice More Questions
Official Correct Answer: C. The diagonals of a parallelogram bisect each other. Hence, the area of $\triangle ABE = \triangle CDE = 12$. The area of $\triangle ADE = \triangle BCE = 12$ as well. Therefore, the total area of the parallelogram is $12 \times 4 = 48$.
Question 18 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsHard
In a rectangle $ABCD , the length is twice the width. If the diagonal $AC$ is $10\ \
5\sqrt{5}
$ , find the area of the rectangle.
Practice More Questions
Official Correct Answer: B. Let the width be $w$. Then the length is $2w$. The diagonal $AC$ is given by $\sqrt{w^2 + (2w)^2} = 10\sqrt{5}$. Simplifying, we get $5w^2 = 500 , so $w^2 = 100$. The area of the rectangle is $2w \times w = 200$.
Question 19 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsHard
In a trapezoid ABCDABCD with AB∥CD,ifAB \parallel CD , ifAB = 10 , CD = 16 , and the height is 6, find the area of the trapezoid.
Practice More Questions
Official Correct Answer: D. The area of a trapezoid is given by $\frac{1}{2} \times (b_1 + b_2) \times h$. Here, $b_1 = 10 , b_2 = 16 , and $h = 6$. So, the area is $\frac{1}{2} \times (10 + 16) \times 6 = 78$.
Question 20 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsHard
In a parallelogram $ABCD , the diagonals intersect at $E$. If the area of $\triangle ABE$ is 15, find the area of the parallelogram.
TITA Answer:
Practice More Questions
Official Correct Answer: 60. The diagonals of a parallelogram bisect each other. Hence, the area of $\triangle ABE = \triangle CDE = 15$. The area of $\triangle ADE = \triangle BCE = 15$ as well. Therefore, the total area of the parallelogram is $15 \times 4 = 60$.
Question 21 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsEasy
In a rectangle, the length is twice the breadth. If the perimeter is 36 cm, what is the length?
Practice More Questions
Official Correct Answer: A. Let breadth = x$. Then length = 2x$. Perimeter = 2(x + 2x) = 36$. So, $6x = 36 \Rightarrow x = 6$. Length = 2 \times 6 = 12$ cm.
Question 22 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsModerate
In a trapezium, the lengths of the parallel sides are 10 cm and 16 cm, and the height is 8 cm. What is the area of the trapezium?
Practice More Questions
Official Correct Answer: B. Area of trapezium = \frac{1}{2} \times (10 + 16) \times 8 = 80$ cm².
Question 23 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsHard
In a parallelogram, the lengths of the sides are 12 cm and 15 cm, and the height corresponding to the 12 cm side is 10 cm. What is the area of the parallelogram?
Practice More Questions
Official Correct Answer: A. Area of parallelogram = base \times height = 12 \times 10 = 120$ cm².
Question 24 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsEasy
A rectangle has a length of 8 cm and a width of 4 cm. What is the area of the rectangle in square centimeters?
Practice More Questions
Official Correct Answer: A. Area of a rectangle is given by length \times width. Substituting the given values gives $8 \times 4 = 32$.
Question 25 of 75
ThinkCAT Practice SetQAGeometry • QuadrilateralsModerate
A parallelogram has a base of 12 cm and a height of 7 cm. What is the area of the parallelogram in square centimeters?
Practice More Questions
Official Correct Answer: A. Area of a parallelogram is given by base \times height. Substituting the given values gives $12 \times 7 = 84$.

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Frequently Asked Questions about CAT Quadrilaterals Practice Questions (75+ Questions)

What concepts are covered in the Quadrilaterals Practice Drills practice module?

This module covers Quadrilaterals with 75 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for Quadrilaterals Practice Drills questions?

The ideal target pace is 1.8 to 2.2 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.

Where can I find official past year CAT papers for Quadrilaterals Practice Drills?

Official past year exam questions are available in our CAT Geometry PYQ Hub module.

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