Free Printable Quadrilaterals

Worksheets

Quadrilaterals

Total questions: 91

Worksheet time: 46mins

Name

Class

Date

Define what a quadrilateral is.

A quadrilateral is a polygon with four sides and four angles.

A quadrilateral is a polygon with three sides and three angles.

A quadrilateral is a polygon with five sides and five angles.

A quadrilateral is a polygon with six sides and six angles.

Name different quadrilateral shapes.

Square, rectangle, parallelogram, rhombus, trapezoid, kite.

Circle, triangle, pentagon, hexagon, octagon, ellipse.

Cube, sphere, cylinder, cone, pyramid, prism.

Line, ray, segment, point, angle, arc.

Solve problems involving square and rectangular shapes. (For example: Find the area of a square with side 4 cm.)

Area of a square = side × side = 4 cm × 4 cm = 16 cm².

Area of a square = side + side = 4 cm + 4 cm = 8 cm².

Area of a square = side × 2 = 4 cm × 2 = 8 cm².

Area of a square = side × side = 4 cm × 4 cm = 8 cm².

What is a quadrilateral? Fill in the blank: A quadrilateral is a plane figure that has ____ sides (edges), four vertices (corners), and interior angles that add to 360 degrees.

four

three

five

six

Which of the following objects are quadrilaterals? (Select all that apply)

Kite

Road sign (right arrow)

Playing card

Popcorn box

Chessboard

Which of the following shapes is NOT a quadrilateral?

Square

Rectangle

Triangle

Rhombus

Fill in the blank: A quadrilateral, also known as _______ or quadrangle, is a general term for a four-sided polygon.

tetragon

pentagon

hexagon

octagon

Which of the following is NOT a type of quadrilateral shown in the hierarchy diagram?

Trapezoid

Parallelogram

Pentagon

Kite

According to the hierarchy diagram, which quadrilaterals are directly classified under parallelogram?

Rectangle and Rhombus

Trapezoid and Kite

Square and Kite

Isosceles Trapezoid and Square

10.

The common parts of a quadrilateral are: ____ – a side is a line segment which joins any two adjacent vertices.

Side

Angle

Diagonal

Vertex

11.

The common parts of a quadrilateral are: ____ – an interior angle is the angle formed between two adjacent sides.

Interior angle

Diagonal

Vertex

Exterior angle

12.

The common parts of a quadrilateral are: ____ – it is the distance between two parallel sides of a quadrilateral.

Height or Altitude

Diagonal

Vertex

Median

13.

The common parts of a quadrilateral are: ____ – this is the side that is perpendicular to the altitude.

Base

Vertex

Diagonal

Angle

14.

The common parts of a quadrilateral are: ____ – this is the line segment joining any two non-adjacent vertices.

Diagonal

Median

Altitude

Bisector

15.

Which type of quadrilateral has two pairs of parallel sides?

Trapezium

Parallelogram

Trapezoid

Rectangle

16.

Which type of quadrilateral has only one pair of parallel sides?

Trapezium

Parallelogram

Trapezoid

Rhombus

17.

Which type of quadrilateral does not have any pair of parallel sides?

Trapezium

Parallelogram

Trapezoid

Square

18.

Rectangle, Rhombus and Square are special types of _________

parallelograms

triangles

trapeziums

circles

19.

Which type of quadrilateral has all angles 90° and opposite sides equal?

Square

Rectangle

Rhombus

Parallelogram

20.

Which type of quadrilateral has all angles 90° and all sides equal?

Square

Rectangle

Rhombus

Parallelogram

21.

Which type of quadrilateral has all sides equal and opposite sides parallel?

Square

Rectangle

Rhombus

Parallelogram

22.

Which type of quadrilateral has opposite sides parallel and equal?

Square

Rectangle

Rhombus

Parallelogram

23.

Which type of quadrilateral has two sides parallel?

Trapezoid/Trapezium

Kite

Parallelogram

Rhombus

24.

Which type of quadrilateral has adjacent pairs of sides equal?

Trapezoid/Trapezium

Kite

Parallelogram

Rhombus

25.

What is the straight line joining the opposite corners of a quadrilateral called?

Diagonal

Median

Altitude

Bisector

26.

Which quadrilateral has two diagonals that are perpendicular and bisect each other?

Rhombus

Rectangle

Square

Trapezoid

27.

Which quadrilateral has two diagonals that bisect each other but are not necessarily perpendicular?

Parallelogram

Rectangle

Rhombus

Square

28.

Which quadrilateral has two diagonals that are perpendicular, equal, and bisect each other?

Square

Rectangle

Rhombus

Trapezium

29.

Which quadrilateral has two diagonals that are equal and bisect each other?

Rectangle

Rhombus

Trapezoid

Parallelogram

30.

Which quadrilateral has two diagonals that are perpendicular, and the longer diagonal bisects the shorter one?

Kite

Parallelogram

Rectangle

Rhombus

31.

Which quadrilateral has two diagonals that are not equal (except in the case of an isosceles trapezoid)?

Trapezoid

Rectangle

Square

Rhombus

32.

What is the formula for the perimeter of a square?

$x^2$

x+4

33.

What is the formula for the perimeter of a rectangle?

2l + 2b

l × b

l + b

2l × b

34.

What is the formula for the perimeter of a parallelogram?

2a + 2b

$a^2 + b^2$

4ab

35.

What is the formula for the perimeter of a rhombus?

$a^2$

a+b+c+d

36.

What is the formula for the perimeter of a kite?

2a + 2b

$a^2 + b^2$

2ab

a + b

37.

What is the formula for the perimeter of a trapezoid?

a + b + c + d

2a + 2b

a + b + 2h

a + b + h + d

38.

Refer to the diagram of the quadrilateral ABCD. Fill in the blank: The formula for the area of a quadrilateral using the lengths of the diagonals e₁ and e₂ and the angle θ between them is _______. Where θ is the angle formed between e₁ and e₂.

A = (1/2) e₁ e₂ sinθ

A = e₁ e₂ cosθ

A = (1/2) e₁ e₂ tanθ

A = e₁ e₂ sinθ

39.

Refer to the diagram of the quadrilateral ABCD. Fill in the blank: The formula for the area of a quadrilateral when the four sides are labeled such that a² + c² > b² + d² is _______.

A = (1/4) (a² + c² - b² - d²) |tanθ|

A = (1/2) (a² + b² + c² + d²) sinθ

A = (1/4) (a² + b² - c² - d²) |tanθ|

A = (1/2) (a² + c² + b² + d²) cosθ

40.

Refer to the diagram of the quadrilateral ABCD. Fill in the blank: The formula for the area of a quadrilateral using the semi-perimeter s and angles A and C (any two opposite angles) is _______.

A = sqrt[(s-a)(s-b)(s-c)(s-d) - abcd cos²(1/2(A+C))]

A = (a+b+c+d)/2 × sin(A+C)

A = (s-a)(s-b)(s-c)(s-d) + abcd sin²(1/2(A+C))

A = sqrt[(s-a)(s-b)(s-c)(s-d) + abcd cos²(1/2(A+C))]

41.

What shape is shown in the image?

Triangle

Circle

Square

Rectangle

42.

Is a square a type of quadrilateral?

Yes

43.

A square has ____ sides.

44.

What is a square?

A) A plane figure of four sides in which all sides are equal, the opposite sides are parallel and diagonals are also equal. The angle between the adjacent sides is a right angle.

B) A plane figure of four sides in which only opposite sides are equal.

C) A plane figure of three sides.

D) A plane figure with no equal sides.

45.

Fill in the blank: The area of a square whose side is 'a' is _______.

$a^2$

$a^4$

46.

Which of the following statements about a square is true?

The diagonals of a square are not equal.

The opposite sides of a square are parallel.

The angle between adjacent sides is not a right angle.

All sides of a square are not equal.

47.

Refer to the diagram of square ABCD where each side is 'a' and AC is a diagonal. What is the area of the square ABCD?

A) a

B) 2a

$a^2$

$2a^2$

48.

Fill in the blank: The diagonal AC divides the square ABCD into two equal ______ triangles.

right

isosceles

scalene

obtuse

49.

What is a square?

A plane figure of four sides in which all sides are equal, the opposite sides are parallel and diagonals are also equal. The angle between the adjacent sides is a right angle.

A plane figure with three sides.

A figure with all sides of different lengths.

A figure with no right angles.

50.

Fill in the blank: The perimeter of a square ABCD with side length 'a' is _______.

$a^2$

51.

Fill in the blank: The diagonal (diameter) of a square ABCD with side length 'a' is _______.

a√2

a/2

$a^2$

52.

Which of the following is true about the diagonals of a square?

They are equal in length

They are not equal

They are perpendicular bisectors

Both A and C

53.

Refer to the diagram of square ABCD where each side is 'a' and diagonal AC is 'd'. What is the value of 'd'?

A) a

B) 2a

C) a√2

D) a/2

54.

The diagonal of a square base plate is 25 cm. Find the length of the plate and its area.

Length of the plate = $25/\sqrt{2}$ = 17.68 cm (rounded to 2 decimal places); Area = $(17.68)^{2}$ = 312.5 sq. cm (rounded to 1 decimal place)

Length of the plate = $25/2$ = 12.5 cm; Area = $(12.5)^2$ = $156.25$ sq. cm

Length of the plate = 25 cm; Area = (25)^2 = 625 sq. cm

Length of the plate = $25/\sqrt{3}$ = 14.43 cm; Area = $(14.43)^{2}$ = 208.3 sq. cm

55.

A square lawn whose area is 200 sq. m has to be enclosed within iron railing. Find the length of the railing and its cost at PHP 250 per meter.

Length of railing (perimeter) = 4 × √200 = 56.57 m (rounded to 2 decimal places); Cost = 56.57 × 250 = PHP 14,142.50

Length of railing (perimeter) = 4 × √100 = 40.00 m; Cost = 40.00 × 250 = PHP 10,000.00

Length of railing (perimeter) = 4 × √150 = 48.99 m; Cost = 48.99 × 250 = PHP 12,247.50

Length of railing (perimeter) = 4 × √250 = 63.25 m; Cost = 63.25 × 250 = PHP 15,812.50

56.

A piece of wire 72 cm long is cut into two equal parts. Each part is bent to form a square. If the total area of the two squares formed is 164 cm², find the difference in lengths of the two parts.

8 cm

6 cm

10 cm

12 cm

57.

What is the formula for the area of a rectangle?

Area = Length × Width

Area = 2 × (Length + Width)

Area = Length × Length

Area = Width × Width

58.

Which of the following statements is true about a rectangle?

Opposite sides are parallel and equal in length

Diagonals are not equal

Angles between adjacent sides are not right angles

Diagonals do not bisect each other

59.

Fill in the blank: The diagonals of a rectangle are ______ and bisect each other.

equal

perpendicular

parallel

unequal

60.

The angles between adjacent sides of a rectangle are right angles.

True

False

61.

What is a rectangle?

A four sided figure whose opposite sides are parallel and equal in length, diagonals are equal and angles between adjacent sides are right angles. Also diagonals of rectangle bisect each other.

A three sided figure with equal sides.

A figure with all sides of different lengths.

A circle with equal diameter.

62.

Fill in the blank: The area of a rectangle is _________.

Length x Width

Length + Width

2 x (Length + Width)

Length x Height

63.

Fill in the blank: The formula for the perimeter of a rectangle is _________.

P = 2(L + W)

P = L × W

P = 4L

P = 2L + W

64.

Fill in the blank: The formula for the diagonal of a rectangle is _________.

d = √(l² + w²)

d = l + w

d = 2(l + w)

d = l × w

65.

The diagonals of a rectangle are equal and bisect each other.

True

False

66.

The angles between adjacent sides of a rectangle are right angles.

True

False

67.

The area of a rectangle is 20 sq. cm and its width is 4 cm long. What is the length of the rectangle?

5 cm

6 cm

8 cm

4 cm

68.

A soccer field is 13 m long and 10 m wide. It has a concrete path 3.5 m wide around it. What is the area of the cement path?

161.5 m²

150 m²

120 m²

91.5 m²

69.

A square has sides measuring 31 cm. Find its area, diagonal, and perimeter.

Area = 961 cm², Diagonal = 31√2 cm ≈ 43.84 cm, Perimeter = 124 cm

Area = 961 cm², Diagonal = 31 cm, Perimeter = 124 cm

Area = 961 cm², Diagonal = 62 cm, Perimeter = 93 cm

Area = 961 cm², Diagonal = 31√3 cm ≈ 53.70 cm, Perimeter = 124 cm

70.

The difference between the areas of a square and an equilateral triangle is 18.65 m². If their perimeters are equal, find the sum of their areas.

Sum of their areas ≈ 55.95 m²

Sum of their areas ≈ 40.25 m²

Sum of their areas ≈ 62.10 m²

Sum of their areas ≈ 48.80 m²

71.

A square with sides measuring 20 cm was cut from a larger square. If the area of the former is one-third of the latter, find the dimension of the sides of the larger square.

Dimension of the sides of the larger square = 34.64 cm

Dimension of the sides of the larger square = 30 cm

Dimension of the sides of the larger square = 40 cm

Dimension of the sides of the larger square = 25 cm

72.

The sides of a rectangle are 42m and 59m. Find its diagonal, area and perimeter.

Diagonal = 72.36m, Area = 2478m², Perimeter = 202m

Diagonal = 60.00m, Area = 2480m², Perimeter = 180m

Diagonal = 70.00m, Area = 2500m², Perimeter = 190m

Diagonal = 80.00m, Area = 2600m², Perimeter = 210m

73.

A rectangle has an area of 1,856mm² and a perimeter of 180mm. Find its longer side.

The longer side is 58mm.

The longer side is 32mm.

The longer side is 46mm.

The longer side is 40mm.

74.

The perimeter of a rectangle is 256cm. If the sides are in the ratio 2:5, find its area.

The area is 1,824cm².

The area is 2,560cm².

The area is 3,200cm².

The area is 1,600cm².

75.

What is a parallelogram?

A quadrilateral with all sides equal

A quadrilateral with equal and parallel opposite sides

A quadrilateral with all angles equal

A quadrilateral with no parallel sides

76.

Fill in the blank: The opposite sides of a parallelogram are of ________ length.

equal

different

double

half

77.

Fill in the blank: The opposite angles of a parallelogram are of ________ measure.

equal

different

zero

infinite

78.

In the figure, ABCD is a parallelogram. Which sides are parallel?

A) AB || CD and AD || BC

B) AB || AD and CD || BC

C) AB || BC and AD || CD

D) AB || CD and AB || BC

79.

Fill in the blank: In a parallelogram, ∠A + ∠D = ________°.

180

120

360

80.

Fill in the blank: In a parallelogram, ∠B + ∠C = ________°.

180

120

360

81.

Opposite sides of a parallelogram are parallel and congruent.

True

False

82.

Opposite angles of a parallelogram are congruent.

True

False

83.

The consecutive angles of a parallelogram are supplementary.

True

False

84.

If one angle of a parallelogram is right, then all angles are right.

True

False

85.

The diagonals of a parallelogram bisect each other and each one separates the parallelogram into two congruent triangles.

True

False

86.

Fill in the blank: The ________ Law is associated with parallelograms.

Parallelogram

Pythagoras

Newton's

Ohm's

87.

What does the Parallelogram Law state?

The sum of the square of all the sides of a parallelogram is equal to the sum of the square of its diagonals.

The sum of the angles in a parallelogram is always 360 degrees.

The opposite sides of a parallelogram are always equal and parallel.

The diagonals of a parallelogram bisect each other at right angles.

88.

According to the Parallelogram Law, which of the following equations is correct?

$AB^2 + BC^2 + CD^2 + AD^2 = AC^2 + BD^2$

$AB^2 + BC^2 = AC^2 + BD^2$

$AB^2 + AD^2 = AC^2 + BD^2$

$AB^2 + BC^2 + CD^2 = AC^2 + BD^2$

89.

Fill in the blanks: In a parallelogram, $2a^2 + 2b^2$ = ____ + ____

d1^2 + d2^2

$a^2 + b^2$

2ab

$a^2 + d1^2$

90.

What is the formula for the area of a parallelogram?

Area = base + height

Area = base x height

Area = base / height

Area = base - height

91.

Fill in the blank: The area of a parallelogram is calculated as ______ x height.

base

side

angle

radius

100 %

Quadrilaterals

Total questions: 91

Worksheet time: 46mins

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