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MathematicsClass 8Quadrilaterals

Quadrilaterals | Class 8 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 3 min read

Quadrilaterals – this guide gives you a concise, exam-ready overview of Quadrilaterals from Class 8 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

Square

The square is a special type of rectangle and rhombus where all sides are equal and all angles are 90 degrees. It combines properties of both shapes: equal sides like a rhombus and right angles like a rectangle. The section explains that a square is both equilateral (all sides equal) and equiangular (all angles equal). The diagonals of a square are equal, bisect each other at right angles, and are equal in length. The section introduces formulas for area and perimeter of a square: area = side² and perimeter = 4 × side. Examples include calculating the area and perimeter of squares and identifying squares in real life, such as tiles and chessboards. The section emphasizes the symmetry and special properties of squares in geometry.

📊 Diagram: Diagram shows square ABCD with all sides equal, all angles marked 90°, and diagonals intersecting at right angles and bisecting each other.

🧪 Activity: Activity: Students draw squares of different sizes, measure sides and diagonals, and verify properties.

🔗 Connection: This section connects to the study of rhombuses, another special parallelogram with equal sides but different angle properties.

Frequently asked questions

1. Find all the sides and the angles of the quadrilateral obtained by joining two equilateral triangles with sides 4 cm.

Solution: Each equilateral triangle has all sides equal to 4 cm and all angles equal to 60°. When two equilateral triangles are joined along one side, the quadrilateral formed has:

  • Two sides of length 4 cm (the joined side is common and internal).
  • The other sides are also 4 cm each (the remaining sides of the triangles).
  • The angles at the joined side will be 120° each (since the two 60° angles add up).
  • The other angles remain 60° each.

Thus, the quadrilateral has sides 4 cm, 4 cm, 4 cm,

2. Construct a kite whose diagonals are of lengths 6 cm and 8 cm.

Solution: To construct a kite with diagonals 6 cm and 8 cm: 1. Draw one diagonal of length 8 cm. 2. Find the midpoint of this diagonal. 3. At the midpoint, draw a perpendicular line. 4. On this perpendicular, mark points 3 cm above and below the midpoint (since the other diagonal is 6 cm). 5. Join the endpoints of the 8 cm diagonal to these points to form the kite. 6. Verify that the two pairs of adjacent sides are equal. This construction ensures the kite has diagonals 6 cm and 8 cm intersectin

3. Find the remaining angles in the following trapeziums — 100°, 135°, 105°

Solution: In a trapezium, the sum of the interior angles is 360°. Given angles: 100°, 135°, 105° Sum of given angles = 100 + 135 + 105 = 340° Remaining angle = 360° - 340° = 20° Thus, the missing angle is 20°.

4. Draw a Venn diagram showing the set of parallelograms, kites, rhombuses, rectangles, and squares. Then, answer the following questions — (i) What is the quadrilateral that is both a kite and a parallelogram? (ii) Can there be a quadrilateral that is both a kite and a rectangle? (iii) Is every kite a rhombus? If not, what is the correct relationship between these two types of quadrilaterals?

Solution:

  • Draw a Venn diagram with overlapping sets for parallelograms, kites, rhombuses, rectangles, and squares.

(i) A quadrilateral that is both a kite and a parallelogram is a rhombus because a rhombus has two pairs of adjacent equal sides (kite property) and opposite sides parallel (parallelogram property). (ii) There cannot be a quadrilateral that is both a kite and a rectangle because a kite has two pairs of adjacent equal sides but a rectangle has equal opposite sides and all angles 90

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