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CAT Polygons and Quadrilaterals questions with solutions

Polygons, quadrilaterals and areas. 12 questions from our 2016–2021 CAT pattern papers. Each has the answer and a full solution.

CAT 2021

E is the midpoint of BC and F is the midpoint of CD. What is the area (in cm²) of triangle AEF?CAT 2021 Slot 2 · medium

CAT 2020

ABCDEF is a regular hexagon of side 6 cm. What is the area (in cm²) of triangle ACE?CAT 2020 Slot 1 · medium
ABCDEF is a regular hexagon with side 6 cm.CAT 2020 Slot 2 · hard
ABCDEF is a regular hexagon of side 6 cm.CAT 2020 Slot 3 · medium

CAT 2019

Each interior angle of a regular polygon measures 150°.CAT 2019 Slot 1 · easy

CAT 2018

The line segments AE and BD intersect at F. Find the area (in cm²) of triangle BEF.CAT 2018 Slot 1 · hard
Each interior angle of a regular polygon is 140°. How many diagonals does the polygon have?CAT 2018 Slot 2 · medium

CAT 2017

ABCDEF is a regular hexagon with side 4 cm.CAT 2017 Slot 1 · medium
Each interior angle of a regular polygon is 150°. How many diagonals does the polygon have?CAT 2017 Slot 2 · medium

CAT 2016

Each interior angle of a regular polygon is 156°. How many diagonals does the polygon have?CAT 2016 Slot 1 · medium
ABCD is a rectangle with AB = 8 cm and BC = 6 cm. E is the midpoint of CD. What is the area of triangle AEC?CAT 2016 Slot 1 · medium
Each interior angle of a regular polygon measures 156°.CAT 2016 Slot 2 · medium