Class 8 Maths · Original EZT practice
Quadrilaterals (Class 8 Chapter 4): summary and practice
Four sides, four corners, many shapes. Chapter 4 sorts quadrilaterals by their sides, angles and diagonals. All questions are original EZT tutor practice following the chapter's own section order. Edition note: this page covers the new NCERT book Ganita Prakash (Grade 8). Older Class 8 books numbered chapters differently - check your chapter title, not just the number.
8 original worked examples, 8 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 20 October 2026:
1. Rectangles, squares and the angle sum
The four angles of any quadrilateral add to three hundred sixty degrees - split it into two triangles of one hundred eighty each. A rectangle has four right angles and equal diagonals; a square has four right angles and four equal sides.
2. Parallelograms
A parallelogram has both pairs of opposite sides parallel. Its opposite sides are equal, opposite angles are equal, adjacent angles add to one hundred eighty degrees and the diagonals bisect each other.
3. Rhombus and special cases
A rhombus has four equal sides; its diagonals cross at right angles and bisect each other and its angles. Every square is a rhombus, but not every rhombus is a square.
4. Kite and trapezium
A kite has two pairs of equal adjacent sides, and its diagonals meet at right angles. A trapezium has exactly one pair of parallel sides.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Find a missing fourth angle
Choose the method: Add the known angles and subtract from the quadrilateral total.
EZT practice question
Three angles of a quadrilateral are eighty, ninety-five and one hundred ten degrees. Find the fourth.
Show the worked solution
- The three known angles add to two hundred eighty-five degrees.
- Subtract from three hundred sixty.
Answer: Seventy-five degrees.
Check: Eighty plus ninety-five plus one hundred ten plus seventy-five is three hundred sixty.
Watch for this: Do not subtract from one hundred eighty; that is the triangle total.
Now try it yourself
Three angles are ninety, one hundred and seventy degrees - find the fourth.
Check your answer
One hundred degrees.
Three hundred sixty minus two hundred sixty is one hundred.
Find angles given in a ratio
Choose the method: Share the total among the ratio parts.
EZT practice question
The angles of a quadrilateral are in the ratio one to two to three to four. Find each angle.
Show the worked solution
- The ratio parts total ten.
- Three hundred sixty divided by ten is thirty-six.
Answer: Thirty-six, seventy-two, one hundred eight and one hundred forty-four degrees.
Check: The four angles add to three hundred sixty degrees.
Watch for this: Do not divide by four; divide by the total number of ratio parts.
Now try it yourself
Angles in the ratio one to one to two to two - find the largest.
Check your answer
One hundred twenty degrees.
Six parts share three hundred sixty, so each part is sixty and the largest takes two parts.
Find the angles of a parallelogram from one angle
Choose the method: Use opposite angles equal and adjacent angles supplementary.
EZT practice question
One angle of a parallelogram is seventy degrees. Find the other three.
Show the worked solution
- Opposite angles are equal, so the angle opposite is also seventy.
- Adjacent angles add to one hundred eighty, so each remaining angle is one hundred ten.
Answer: Seventy, one hundred ten and one hundred ten degrees.
Check: Seventy plus seventy plus one hundred ten plus one hundred ten is three hundred sixty.
Watch for this: Do not make all four angles equal; only a rectangle does that.
Now try it yourself
One angle is one hundred twenty-five degrees - find the adjacent angle.
Check your answer
Fifty-five degrees.
Adjacent angles of a parallelogram add to one hundred eighty.
Find the perimeter of a parallelogram
Choose the method: Opposite sides are equal, so double the sum of two adjacent sides.
EZT practice question
A parallelogram has sides of seven cm and four cm. Find its perimeter.
Show the worked solution
- Opposite sides are equal.
- The perimeter is two times seven plus four.
Answer: Twenty-two cm.
Check: Seven plus four plus seven plus four is twenty-two.
Watch for this: Do not count each side only once; each length appears twice.
Now try it yourself
Sides nine cm and five cm - perimeter?
Check your answer
Twenty-eight cm.
Two times nine plus five is twenty-eight.
Find the side of a rhombus from its diagonals
Choose the method: Use the half-diagonals as the legs of a right triangle.
EZT practice question
The diagonals of a rhombus are six cm and eight cm. Find its side.
Show the worked solution
- The diagonals bisect each other at right angles, so the half-diagonals are three and four.
- The side is the hypotenuse of a right triangle with legs three and four.
Answer: Five cm.
Check: Three squared plus four squared is twenty-five, whose square root is five.
Watch for this: Do not add the half-diagonals; use Pythagoras.
Now try it yourself
Diagonals ten cm and twenty-four cm - find the side.
Check your answer
Thirteen cm.
Half-diagonals five and twelve give the hypotenuse thirteen.
Find the perimeter once the side is known
Choose the method: All four sides of a rhombus are equal.
EZT practice question
A rhombus has diagonals of six cm and eight cm. Find its perimeter.
Show the worked solution
- The side is five cm, from half-diagonals three and four.
- All four sides are equal.
Answer: Twenty cm.
Check: Four times five is twenty.
Watch for this: Do not multiply the diagonal lengths; the perimeter uses the side.
Now try it yourself
A rhombus has side thirteen cm - perimeter?
Check your answer
Fifty-two cm.
Four times thirteen is fifty-two.
Find the area of a kite from its diagonals
Choose the method: The area of a kite is half the product of its diagonals.
EZT practice question
The diagonals of a kite are twelve cm and eight cm. Find its area.
Show the worked solution
- The diagonals of a kite meet at right angles.
- The area is half the product of the diagonals.
Answer: Forty-eight square cm.
Check: Half of twelve times eight is forty-eight.
Watch for this: Do not forget the half; the full product double-counts.
Now try it yourself
Diagonals ten cm and six cm - area?
Check your answer
Thirty square cm.
Half of ten times six is thirty.
Name a quadrilateral from its properties
Choose the method: Match the given property to the defining property of each shape.
EZT practice question
Which quadrilateral has exactly one pair of parallel sides?
Show the worked solution
- Parallelograms have two pairs of parallel sides.
- Exactly one pair is the defining property of a trapezium.
Answer: The trapezium.
Check: A trapezium is defined by exactly one pair of parallel sides.
Watch for this: Do not confuse it with a parallelogram, which has two pairs.
Now try it yourself
What do the diagonals of a kite do?
Check your answer
They meet at right angles.
That is a defining diagonal property of a kite.
Try a mixed set
Choose a method or explanation before opening each answer.
1. What is the angle sum of a quadrilateral?
Show answer and reason
Three hundred sixty degrees.
It splits into two triangles.
2. Name two properties of a parallelogram.
Show answer and reason
Opposite sides and opposite angles are equal, and the diagonals bisect each other.
Both pairs of opposite sides are parallel.
3. How do you get a rhombus side from its diagonals?
Show answer and reason
Use the half-diagonals as the legs of a right triangle; the side is the hypotenuse.
The diagonals bisect each other at right angles.
4. What is a trapezium?
Show answer and reason
A quadrilateral with exactly one pair of parallel sides.
Two pairs would make it a parallelogram.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Three angles of a quadrilateral are eighty-five, ninety-five and one hundred degrees - find the fourth.
- The diagonals of a rhombus are sixteen cm and thirty cm. Find its side.
- One angle of a parallelogram is sixty-five degrees. Find the other three.
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Questions about this practice page
- What is the angle sum of a quadrilateral?
- Three hundred sixty degrees.
- What are the properties of a parallelogram?
- Opposite sides and opposite angles are equal, adjacent angles add to one hundred eighty degrees, and the diagonals bisect each other.
- How do I find the side of a rhombus from its diagonals?
- Use the half-diagonals as the legs of a right triangle; the side is the hypotenuse.
- What is a trapezium?
- A quadrilateral with exactly one pair of parallel sides.
- Are these the NCERT exercise questions for Quadrilaterals (Class 8)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.