GRADE 6 ADVANCE GEOMETRY TO LEARN AT SCHOOL

GEOMETRIC
TRANSFORMAT
ION
DEFINITIONS,TYPE,EXAMPLES AND QUIZ

Geometric
Transformation
• The changes we make to the position, size, or
shape of geometric figures including triangles,
squares, circles, or any other shape.
WHAT ARE
GEOMETRIC
TRANSFORMATION?

Translation
Reflection
Rotation
Dilation
1.
2.
3.
4.
Types of Geometric
Transformation

1. TRANSLATION
• A type of geometric transformation where we move or
slide a figure from one place to another without
rotating or changing its size.
• This movement occurs in a straight line, either
horizontally, vertically, or diagonally.
• Every point of the figure shifts by the same distance and in
the same direction along parallel lines.

2. REFLECTION
• Reflection is a geometric transformation where we flip a
figure across a line called "the line of reflection.“
• This creates a mirror image that keeps the original size
and shape of the figure but appears flipped or mirrored.

3. ROTATION
• Rotation is a geometric transformation where we turn a
figure around a fixed point called the "center of
rotation."

3. ROTATION
• The direction of rotation can either be clockwise or
counterclockwise.

4. DILATION
• A geometric transformation where we change the size of
a figure but keep its shape.
• The resulting figure can either enlarge or shrink.
• In dilation, we move each point away from or towards a
fixed center, called “the center of dilation”, and scale by a
factor that determines how much larger or smaller the
figure gets.

WHAT HAPPENED TO THE POLYGON
6
4
6
75
4 125°
80°
80°
12
8
1
2
75°
8 125°
80°
80°

IS IT AN EXAMPLE OF DILATION OR
NOT?
All sides are in
the same ratio
All angles are
equal
Two sides are
in the same ratio
and the included
angles are equal
Right triangles with
hypotenuse and one
side are in the same
ratio
4 2
4
4
2
2
9
3
3
75°
1
75°
30°
35°
115°
35°
30° 115°
8 16 1
2
6
hypotenuse

Two figures are similar
if the second figure
was taken or created
from a rotation,
reflection, translation,
or dilation.
A ____ is when a
figure has increased
or decreased in the
same ratio.
5 5
5
5
15 15
15
15
? ? ?
?

Geometric
Transformation
Formula

EXAMPLE
Translate the point (2,3) by =4and
𝑃 𝑎
= 2.
𝑏 −
1. TRANSLATION

EXAMPLE
Rotate the point (1,2) 90°
𝑄
counterclockwise around the origin.
2. ROTATION

EXAMPLE
Reflect the point ( 3,4) over the x-axis.
𝑅 −
3. REFLECTION

EXAMPLE
Dilate the point (2,3) with a scale factor
𝑆
of =2
𝑘
4. DILATION

AREA OF
TRIANGLES

TRIANGLE
• a triangle is a closed shape that has three sides
and three vertices.
WHAT?
AREA OF A
TRIANGLE
• The total space occupied within the three sides of a
triangle. Basically, it is equal to half of the base
times height.

• To find the area of a tri-sided polygon, we have to know the base (b)
and height (h) of it.
• The base and height of the triangle are perpendicular to each other.
• The unit of area is measured in square units ().

EXAMPLE
What is the area of a triangle with base b
= 3 cm and height h = 4 cm?
Area of a Triangle

Area of Right-Angled Triangle
• A right-angled triangle, also called a right triangle has any one angle
equal to 90°.
• Therefore, the height of the triangle will be the length of the
perpendicular side.

Area of an Equilateral Triangle
• a triangle where all the sides are equal.

Area of an Isosceles Triangle
• An isosceles triangle has two of its sides equal and also the angles
opposite the equal sides are equal.

EXAMPLE
Find the area of an acute triangle with a
base of 13 inches and a height of 5
inches.
Area of a Triangle

EXAMPLE
Find the area of a right-angled triangle
with a base of 7 cm and a height of 8 cm.
Area of a Triangle

EXAMPLE
Find the area of an obtuse-angled
triangle with a base of 4 cm and a height
7 cm.
Area of a Triangle

AREA OF A
QUADRILATER
ALS

QUADRILATERAL
• a polygon with four sides, four angles and four vertices.
WHAT?
PROPERTIES
• Every quadrilateral has 4 vertices and 4 sides enclosing 4 angles.
• The sum of its interior angles is 360 degrees.
• A quadrilateral, in general, has sides of different lengths and angles of
different measures. However, squares, rectangles, parallelograms, etc. are
special types of quadrilaterals with some of their sides and angles being
equal.

1. For Square
AREA OF QUADRILATERAL
FORMULA
A

2. For Rectangle
FORMULA
A

3. For Parallelogram
FORMULA
A

4. For Rhombus
FORMULA
A

5. For Trapezium
FORMULA
A

1. Using Heron’s Formula
FORMULA
A

EXAMPLE
In the given quadrilateral ABCD, the side BD
= 15 cm and the heights of the triangles
ABD and BCD are 5 cm and 7 cm,
respectively. Find the area of the
quadrilateral ABCD.
Area of a
Quadrilateral

EXAMPLE
In the given quadrilateral ABCD, the side BD =
15 cm and the heights of the triangles ABD
and BCD are 5 cm and 7 cm, respectively. Find
the area of the quadrilateral ABCD.

EXAMPLE
Find the area of a rhombus whose
diagonals are 7 cm and 6 cm
respectively.
Area of a
Quadrilateral

EXAMPLE
Find the area of a rhombus whose
diagonals are 7 cm and 6 cm respectively.
Area of a
Quadrilateral

EXAMPLE
Find the area of a rectangle whose
length is 12 cm and breadth is 9 cm.
Area of a
Quadrilateral

ANSWER PLEASE!
Find the area of each
Quadrilateral

AREA OF A
CIRCLES

Area of a Circle
• the region occupied by the circle in a two-
dimensional plane.
WHAT?

EXAMPLE
Find the area of circle if the radius is 7
cm.
Area of a Circle

EXAMPLE
If the diameter of a circle is 12 cm, then
find the area of circle.
Area of a Circle

EXAMPLE
What is the area of a circle with radius 3
cm, in terms of π?
Area of a Circle

EXAMPLE
Find the area of a circular region whose
radius is 21 m.
Area of a Circle

SURFACE AREA
OF A PRISMS

PRISMS
• a polyhedron with 2 polygonal bases parallel to
each other.
WHAT?
SURFACE AREA OF A PRISMS
• the sum of the area of the 2 polygonal bases and
the area of the lateral faces.

1. For RECTANGULAR PRISM
SURFACE AREA OF PRISMS
FORMULA
A

2. For TRIANGULAR PRISM
FORMULA
A)

3. For Pentagonal PRISM
FORMULA
A

4. For Hexagonal PRISM
FORMULA
A

EXAMPLE
What will be the surface area of a
triangular prism if the apothem length,
base length and height are 7 cm, 10 cm
and 18 cm respectively ?
Surface Area of a
Prism

EXAMPLE
Calculate the surface area of a pentagonal
prism with apothem length, base length
and height as 12 cm, 15 cm, and 21 cm
respectively ?
Surface Area of a
Prism

ANSWER PLEASE!
Find the Surface area of each
Prism

SURFACE AREA
OF A
PYRAMIDS

PYRAMID
• a three-dimensional
shape whose base
should be a polygon,
and its face should
be a triangle.
WHAT?

SURFACE AREA OF A
PYRAMID
• the sum of the areas of all faces of a pyramid.
WHAT?

1. For Triangular Pyramid
SURFACE AREA OF PYRAMID
FORMULA
• In the triangular pyramid, the base of the pyramid is a
triangle.

EXAMPLE
Surface Area of a Pyramid

2. For SQUARE Pyramid
FORMULA
• In the Square pyramid, the base of the pyramid is a
square.

3. For PENTAGONAL Pyramid
FORMULA
• In the pentagonal pyramid, the base of the pyramid is a
pentagon.

4. For HEXAGONAL Pyramid
FORMULA
• In the hexagonal pyramid, the base of the pyramid is a
hexagon.

ANSWER PLEASE!
Pyramid

SURFACE AREA
OF A CONE

WHAT?
AREA OF A CONE
• the complete area covered by its two surfaces, i.e.,
circular base area and lateral (curved) surface area

EXAMPLE
Surface Area of a Cone

SURFACE AREA
OF A CYLINDER

CYLINDER
• a three-dimensional structure having circular bases which
are parallel to each other. It does not have any vertices.
WHAT?
AREA OF A
CYLINDER
• the sum of the curved surface and the area of two
circular bases of the cylinder.

EXAMPLES
CYLINDER

SURFACE AREA
OF A SPHERE

SPHERE
• a three-dimensional solid having a round shape,
just like a circle.
WHAT?
AREA OF A SPHERE
• the region covered by its outer surface in three-
dimensional space.

EXAMPLES
SPHERE

VOLUME OF A
PRISMS

VOLUME OF PRISM
WHAT?
• the amount of space a prism occupies.
• A prism is a solid 3-D shape that has two same
faces and other faces that resemble a
parallelogram.

1. TRIANGULAR PRISM
VOLUME OF PRISM FORMULA
𝑽 = 𝑨𝑹𝑬𝑨 ∗ 𝑯𝑬𝑰𝑮𝑯𝑻

2. SQUARE PRISM
𝑽 = 𝑯 𝟑

2. RECTANGULAR PRISM
𝑽=( 𝑨𝑹𝑬𝑨 𝑶𝑭 𝑹𝑬𝑪𝑻𝑨𝑵𝑮𝑳𝑬)∗ 𝑯𝑬𝑰𝑮𝑯𝑻

ANSWER PLEASE!
Find the VOLUME of each
PRISM

VOLUME OF A
PYRAMIDS

PYRAMID
• polyhedron figure which has only one base.
WHAT?
VOLUME OF A PYRAMID
• depends upon the type of pyramid’s base, whether
it is a triangle, square or rectangle.

1. TRIANGULAR PYRAMID
VOLUME OF PYRAMID FORMULA
𝑽 =
𝟏
𝟔
( 𝑨𝑹𝑬𝑨 ) ∗ 𝒉

1. SQUARE PYRAMID
𝑽 =
𝟏
𝟑
𝒂
𝟐
∗ 𝒉

1. RECTANGULAR PYRAMID
𝑽 =
𝟏
𝟑
𝒍 ∗ 𝒘 ∗ 𝒉

VOLUME OF A
CONE

CONE
• a three-dimensional geometric shape having a
circular base that tapers from a flat base to a point
called apex or vertex.
WHAT?
VOLUME OF A
CONE
• the space or the capacity of the cone.

ANSWER PLEASE!
CONE

VOLUME OF A
SPHERE

SPHERE
• defined as the three-dimensional round solid
figure in which every point on its surface is
equidistant from its centre.
WHAT?
VOLUME OF A
SPHERE
• the amount of space occupied, within the sphere.

ANSWER PLEASE!
SPHERE

GRADE 6 ADVANCE GEOMETRY TO LEARN AT SCHOOL

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