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CAT 2025 Slot 3 QA Question 18

Multiple choice (+3 / −1) · Geometry · Quadrilaterals · Try it, then check the answer and solution below.

CAT 2025 Slot 3QAGeometry • QuadrilateralsHard
ABCD is a trapezium in which AB is parallel to DC, AD is perpendicular to AB, and AB = 3DC. If a circle inscribed in the trapezium touching all the sides has a radius of 3 cm, then the area, in sq. cm, of the trapezium is
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Answer and solution

Answer: A) 48

📌 Core Concept
For a trapezium to have an inscribed circle (be tangential), the sum of the lengths of the two parallel sides equals the sum of the lengths of the two non-parallel sides. The area of a trapezium is given by: $Area=(AB+DC)×h2\text{Area} = \frac{(AB + DC) \times h}{2} where hh is the height.
🔢 Step-by-Step Solution
1
Given Data:
AB∥DCAB \parallel DC
AD⊥ABAD \perp AB (height h=6h = 6 \text{ cm}, since radius r=3r = 3 \text{ cm})
AB=3×DCAB = 3 \times DC
Radius of inscribed circle r=3r = 3 \text{ cm}
2
Let DC = x , then AB=3xAB = 3x.
3
Sum of Bases:
AB+DC=3x+x=4xAB + DC = 3x + x = 4x
4
Sum of Non-parallel Sides:
AD+BC=6+BCAD + BC = 6 + BC
Since the trape

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