Question

Identify the type of polygon represented in the figure given below.

• A. 1 is concave, 2 is convex
• B. 1 is convex, 2 is concave
• C. Both are concave and convex quadrilaterals
• D. They are neither concave nor convex.

Answer 1

The correct option is A 1 is concave, 2 is convex

Quadrilateral ABCD is said to be convex, if no portion of their diagonals is in the exterior.

Quadrilateral ABCD is said to be concave, if at least one portion of their diagonals is in exterior.

In (1), A and C are non-consecutive points. When we join A and C, the line segment lies outside the polygon. Hence, (1) is a concave polygon.

In (2), when we join either A and C or B and D, the line segments AC and BD lies inside the polygon. Hence, (2) is a convex polygon.

Hence first polygon is concave while the second one is a convex polygon.