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CAT Types of Quadrilaterals - Practice Questions & MCQ

Edited By admin | Updated on Oct 04, 2023 04:20 PM | #CAT

Syllabus

Quick Facts

6 Questions around this concept.

Solve by difficulty

EASY

A rectangle is a quadrilateral that has all four angles equal to 90. (True/False)

True

False

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In a rectangle, both diagonals bisect each other at 90°. (True/False)

True

False

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Each angle of a rectangle is a/an:

acute angle

obtuse angle

right angle

reflex angle

View Solution

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Concepts Covered - 1

Types of Quadrilaterals

Rectangle: A rectangle is a parallelogram that has all four angles equal to 90^∘ .

A summary of the properties of a rectangle is:

Both pairs of opposite sides are parallel.
Both pairs of opposite sides are of equal length.
Both diagonals bisect each other.
Diagonals are equal in length.
All angles at the corners are right angles.

Area of rectangle = Length × Breadth

Length of the rectangle = AB

Length of the Breadth = BC

Rhombus: A rhombus is a parallelogram that has all four sides of equal length.

A summary of the properties of a rhombus is:

Both pairs of opposite sides are parallel.
All sides are equal in length.
Both pairs of opposite angles are equal.
Both diagonals bisect each other at 90^∘ .
Diagonals of a rhombus bisect both pairs of opposite angles.

Area of rhombus when base and height are given

Area = Base × Height

Area of rhombus when the length of diagonals are given

$\text{Area of rhombus }=\frac{1}{2}\times d_1\times d_2$

Here, d₁ and d₂ ane diagonals of the rhombus.

Square: A square is a rhombus that has all four angles equal to 90^∘.

A summary of the properties of a square is:

Both pairs of opposite sides are parallel.
All sides are equal in length.
All angles are equal to 90^∘ .
Both pairs of opposite angles are equal.
Both diagonals bisect each other at 90^∘ .
Diagonals are equal in length.
Diagonals bisect both pairs of opposite angles (ie. all 45^∘ ).

Area of square = a × a = a²

a = side of a square.

If diagonal, d of a square is given, then

$\text{Area of square }=\frac{1}{2}\times d\times d=\frac{1}{2}\times d^2$

Kite: A kite is a quadrilateral with two pairs of adjacent sides equal. Quadrilateral ACBD is a kite, in which AC = CB and AD = DB

A summary of the properties of a kite is:

Two pairs of adjacent sides are equal in length.
One pair of opposite angles are equal where the angles are between unequal sides.
One diagonal bisect the other diagonal and one diagonal bisect one pair of opposite angles.
Diagonals intersect at right-angles.

$\text{Area of kite }=\frac{1}{2}\times d_1\times d_2$