CAT 2020 Question Paper | Quants Slot 3

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

Video Explanation

Explanatory Answer

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"

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