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Quadrilaterals Quiz - CBSE Class 6 Mathematics

Free practice quiz: Quadrilaterals (CBSE Class 6 Mathematics). 10 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 6 Mathematics practice quiz has 10 multiple-choice questions on Quadrilaterals, and 10 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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What makes a quadrilateral

A quadrilateral is a closed figure with four straight sides, four vertices and four angles.
Types include trapezium, parallelogram, rectangle, rhombus, square and kite. Triangles and pentagons are not quadrilaterals.
A trapezium has at least one pair of parallel sides. A parallelogram has both pairs of opposite sides parallel.

Sum of interior angles

\[\angle A + \angle B + \angle C + \angle D = 360^\circ\]

Common mistake: Thinking a trapezium needs equal sides. It only needs one pair of parallel sides. Its side lengths can all be different.

Can the quadrilateral exist?

Four lengths make a quadrilateral only if every side is shorter than the sum of the other three.
It is enough to check the longest side against the total of the remaining three sides.

Existence rule (each side)

\[a < b + c + d\]

Quick check with longest side d

\[d < a + b + c\]

Common mistake: Comparing the longest side with only one or two other sides instead of the sum of all three others.

Perimeter and area formulas

Perimeter is the total length around the shape. Area is the surface it covers, in square units.
For a parallelogram, the height is the perpendicular distance between the base and its opposite side.

Area of rectangle

\[A = l \times b\]

Perimeter of rectangle

\[P = 2(l + b)\]

Side of square from perimeter

\[a = \frac{P}{4}\]

Area of parallelogram

\[A = b \times h\]

Common mistake: Using the slanted side instead of the perpendicular height when finding the area of a parallelogram.

Properties of diagonals

Parallelogram diagonals bisect each other. Rectangle diagonals are also equal in length.
Rhombus diagonals bisect each other at right angles but are usually unequal. Square diagonals are equal and perpendicular.

Rhombus diagonals meet at right angles

\[d_1 \perp d_2\]

Area of rhombus

\[A = \frac{1}{2} d_1 d_2\]

Common mistake: Assuming rhombus diagonals are always equal. They are equal only when the rhombus is a square.

Quadrilateral inside a circle

If all four vertices lie on a circle, it is called a cyclic quadrilateral.
In a cyclic quadrilateral, each pair of opposite angles adds up to a straight angle.

First pair of opposite angles

\[\angle A + \angle C = 180^\circ\]

Second pair of opposite angles

\[\angle B + \angle D = 180^\circ\]

Common mistake: Adding adjacent angles instead of opposite angles when using the cyclic quadrilateral rule.

Exam tips

Draw a rough labelled figure before solving any shape question.
Write area answers in square units, such as cm², and perimeter answers in cm.
For side-length questions, always check the existence rule before choosing an answer.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

What is a quadrilateral?
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Answer: B. A four-sided figure
A quadrilateral is defined as a polygon that has four sides, four vertices, and four angles.
What is the sum of the interior angles of a quadrilateral?
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Answer: B. 360 degrees
The sum of the interior angles of a quadrilateral can be calculated with the formula (n-2) × 180 degrees, where n is the number of sides. For a quadrilateral, n=4. Thus, (4-2) × 180 = 360 degrees.
What is the formula to find the area of a rectangle?
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Answer: B. Length x Width
The area of a rectangle is calculated by multiplying the length by the width (A = l × w).
A parallelogram has a base of 10 cm and a height of 5 cm. What is its area?
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Answer: C. 50 cm²
The area of a parallelogram is calculated using the formula A = base × height. Thus, A = 10 cm × 5 cm = 50 cm².
If the diagonals of a rhombus intersect at right angles, what can be said about the lengths of the diagonals?
Show answer
Answer: C. They are perpendicular.
In a rhombus, the diagonals always bisect each other at right angles, meaning they are perpendicular.

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