CAT Quadrilaterals & polygons Questions

Quadrilateral and polygon questions use angle sums, diagonals and special-shape properties. Dividing a shape into triangles can make both area and angle calculations more transparent.

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Key concepts

• Interior and exterior angle sums
• Parallelograms, rectangles, rhombi and trapezia
• Diagonals and triangulation

CAT quadrilaterals & polygons practice questions

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Common mistakes

• Applying a regular polygon property to an irregular polygon.
• Assuming all quadrilaterals have perpendicular diagonals.

Practical solving approaches

• Identify the exact shape from the stated conditions.
• Draw a useful diagonal and calculate smaller triangle areas or angles first.

Quadrilaterals & polygons FAQs

What is the interior angle sum of a polygon?

For a simple polygon with n sides, the interior angles sum to (n − 2) × 180 degrees.

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CAT Quadrilaterals & polygons Questions

Quadrilateral and polygon questions use angle sums, diagonals and special-shape properties. Dividing a shape into triangles can make both area and angle calculations more transparent.

4 free practice questions

Key concepts

• Interior and exterior angle sums
• Parallelograms, rectangles, rhombi and trapezia
• Diagonals and triangulation

CAT quadrilaterals & polygons practice questions

Question 1Multiple choiceMEDIUM

Question 1

Select the correct alternative from the given choices.

Answer the questions independently of each other.

What is the approximate difference between the areas of the largest square that can be inscribed in a regular octagon of side 1 cm and the smallest square that can be inscribed in the same octagon? (cos 22.5° = 0.92)

Choose an answer

A.0.95 cm²B.1.02 cm²C.0.49 cm²D.1.42 cm²

Check answerView solution

Question 2Multiple choiceMEDIUM

Question 2

Select the correct alternative from the given choices.

Answer the questions independently of each other.

A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?

Choose an answer

A.

B.

C.

D.

Check answerView solution

Question 3Multiple choiceMEDIUM

Question 3

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Reena is drawing a polygon. After completing the figure, she observed that the number of diagonals for that polygon is same as the number of its sides. Which figure did she draw?

Choose an answer

A.TriangleB.QuadrilateralC.PentagonD.Hexagon

Check answerView solution

Question 4Type in the answerMEDIUM

Question 4

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

A square has side 16 cm. A second square is drawn inside this square by joining the mid-points of the sides of the square. A third square is drawn by joining the mid-points of the second square. This process is continued indefinitely. Find the sum of the areas of all the squares.

Your answer

Check answerView solution

Common mistakes

• Applying a regular polygon property to an irregular polygon.
• Assuming all quadrilaterals have perpendicular diagonals.

Practical solving approaches

• Identify the exact shape from the stated conditions.
• Draw a useful diagonal and calculate smaller triangle areas or angles first.

Quadrilaterals & polygons FAQs

What is the interior angle sum of a polygon?

For a simple polygon with n sides, the interior angles sum to (n − 2) × 180 degrees.

More Geometry practice

• Circles →
• Coordinate geometry →
• Lines, angles & triangles →
• Mensuration (3D solids) →