# CAT 2020 Question Paper | Quants Slot 3

###### CAT Previous Year Paper | CAT Quants Questions | Question 24

This question is from Geometry. In this question, we need to find the area of the trapezium. CAT Geometry is an important topic with lots of weightage in the CAT Exam. In CAT Exam one can generally expect 4-6 questions from Geometry. Make sure you master Geometry problems by solving CAT Previous Year Paper.

Question 24 : In a trepezium ABCD, AB is parallel to DC, BC is perpendicular to DC and ∠BAD = 45°. If DC = 5 cm, BC = 4 cm, the area of the trepezium in sq. cm is

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Let's draw the Trapezium.

Now drop a perpendicular from D on to AB touching AB at E.

In ΔAED, ∠AED = 90°, ∠DAE = 45°, therefore ∠EDA = 45°.
Clearly ΔAED is an iscoceles right triangle and Quadrilateral BCDE is a rectangle.
Therefore, BC = DE = 4cm.
Since ΔAED is an iscoceles triangle, AE = ED = 4cm.

Area of the Trepezium = Area of ΔAED + Area of Rectangle BCDE
Area of the Trepezium = $$frac{1}{2}$ × AE × ED + DC × BC Area of the Trepezium = $\frac{1}{2}$ × 4 × 4 + 5 × 4 Area of the Trepezium = 8 + 20 Area of the Trepezium = 28 cm2 The question is "In a trepezium ABCD, AB is parallel to DC, BC is perpendicular to DC and ∠BAD = 45°. If DC = 5 cm, BC = 4 cm, the area of the trepezium in sq. cm is" ##### Hence, the answer is, "28" ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Questions | CAT Quantitative Aptitude ## CAT Questions | Verbal Ability for CAT ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Mobile:$91) 99626 48484 / 94459 38484
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