RD Sharma Solutions for Class 6 Maths Chapter 13: Quadrilateral

Chapter 13-Quadrilateral explains the types and formulas required to determine the sides and angles of a quadrilateral. In practice, a quadrilateral is defined as a closed two-dimensional shape that has four sides and four corners and angles. A quadrilateral is obtained by joining four points, among which three are non-collinear. Unlike triangles, the sum of all interior angles of the quadrilateral is 360°. While naming the quadrilateral, the order of the vertices plays a crucial role. In addition, the properties of sides classify the shapes that they possess.

Further, quadrilaterals can be classified into seven types: parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid, each varying with a specific property. A quadrilateral containing only one pair of parallel sides is called a trapezium. Its adjacent angle adds up to 180°. If the two non-parallel opposite sides are of equal length, it is called an isosceles trapezium with equal diagonal length. A quadrilateral with opposite parallel sides is called a parallelogram. The quadrilaterals having all sides equal are defined as a rhombus, whose diagonals bisect each other at right angles. A quadrilateral can also be classified into a concave and a convex quadrilateral.

This chapter further discusses the classifications based on the angles. Quadrilaterals can also be classified based on their angles, such as a quadrilateral, whose each angle is a right angle is a rectangle. Its diagonals bisect each other. A quadrilateral whose every angle measures 90° and whose all sides are equal is a square with two equal diagonals, and they are perpendicular to each other. A quadrilateral having two pairs of equal adjacent sides but unequal opposite sides is called a kite.

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