Concept Scroll LogoConceptScroll
Join or Sign In
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.

Trapezium

The trapezium is a quadrilateral with exactly one pair of parallel sides. This section explains the properties of trapeziums, including that the non-parallel sides are called legs, and the parallel sides are called bases. The sum of interior angles is 360 degrees, as with all quadrilaterals. The section introduces the formula for the area of a trapezium: area = (1/2) × (sum of parallel sides) × height, where height is the perpendicular distance between the parallel sides. The section includes diagrams illustrating these concepts and examples calculating the area and perimeter of trapeziums. Trapeziums are common in real life, such as in the shape of certain bridges, ramps, and tables.

📊 Diagram: Diagram shows trapezium ABCD with AB and DC as parallel sides (bases), AD and BC as legs, and height drawn perpendicular between AB and DC.

🧪 Activity: Activity: Students measure dimensions of trapezium-shaped objects and calculate their area and perimeter.

🔗 Connection: This section concludes the study of quadrilaterals and prepares students for exercises and problem-solving involving all types.

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

Ready to ace this chapter?

Get the full Quadrilaterals chapter — interactive notes, diagrams, worked solutions, polls and a free practice quiz — in the ConceptScroll app.

Open in ConceptScroll →

Study smarter with ConceptScroll

Daily NCERT-aligned reels, AI doubt solving and chapter quizzes — all free.

Start learning free
#cbse notes#class 8#mathematics#ncert

Continue reading

← All articles