THUYÊT TRÌNH DIỆN TÍCH VÀ THỂ TÍCH BẰNG TIẾNG ANH area volume

Square: A 4-sided regular polygon with all sides equal and all internal angles 90°Square: hình vuông Regular polygon: đa giác đều Length: chiều dài... Equilateral Triangle: A triangle wh

AREA & VOLUME

Instructors :…

Presentation group 4: …

w  is the width

h  is the height

Rectangle: A 4-sided polygon where all interior angles are 90°

Rectangle: Hình chữ nhật Width: Chiều rộng Side: cạnh

Interior angle: góc phía trong Height: Chiều dài

Square: A 4-sided regular polygon with all sides equal and all internal angles 90°

Square: hình vuông Regular polygon: đa giác đều Length: chiều dài

Obtuse Triangle

A triangle where one of the internal angles is obtuse (greater than 90 degrees).

Acute triangle: A triangle where all

three internal angles are acute (less than 90 degrees).

01

02

03

04 Right Triangle: A triangle where

one of its interior angles is a  right angle (90 degrees).

Isosceles Triangle:

A triangle which has two of its sides

equal in length.

Equilateral Triangle: A triangle which

has all three of its sides equal in length.

Triangle: A closed figure consisting of three

line segments linked end-to-end

Area of a triangle

The area of a triangle is given by the formula below

Where

 a  is the length of the base

 h  is the length of the corresponding altitude

Triangle: Tam giác Base: Đáy

Corresponding: Tương ứng Altitude: Chiều cao

Heron's Formula for the area of a triangle (Hero's Formula)

A method for calculating the area of a triangle when you

know the lengths of all three sides

● Let a,b,c be the lengths of the sides of a triangle The

area is given by:

where p is half the perimeter, or 

Half the perimeter: Nửa chu vi

Area of an equilateral triangle

The area of an equilateral triangle (all sides congruent)

can be found using the formula

where s is the length of one side of the triangle.

Equilateral triangle: tam giác đều Congruent: Đồng/ đều/ cùng kích thước

Area of a parallelogram

The area of a parallelogram is given by the formula

Area=b.a

b is the length of any base

a is the corresponding altitude

Parallelogram: A quadrilateral with both pairs of opposite sides parallel.

Parallel: song song

Parallelogram: Hình bình hành

Area of a rhombus

1 The "base times height" method

The area of a rhombus is given by the formula:

area=b.a

where

b is the length of the base

a is the altitude (height).

Rhombus : A quadrilateral with all four sides equal in length.

Perpendicular: vuông góc

Distance: khoảng cách

Area of a rhombus

2 The "diagonals" method

Another simple formula for the area of a rhombus when you know the lengths of the diagonals The area is half the product of the diagonals As a formula:

where

d1 is the length of a diagonal

d2 is the length of the other diagonal

Diagonal: đường chéo

Area of a rhombus

3 Using trigonometry

If you are familiar with trigonometry, there is a handy formula when you know the length of a side and any angle:

where

s is the length of any side

a is any interior angle

sin  is the sine function

Trigonometry: lượng giác Handy: hữu ích

Area of an inscribed (cyclic) quadrilateral.

Brahmagupta's Formula

A formula for calculating the area of an inscribed, or cyclic quadrilateral

when you know the lengths (a,b,c,d) of the sides

Where a,b,c,d are side lengths, and p is half the perimeter:

Inscribed (cyclic) quadrilateral: A quadrilateral where all four vertices lie on a common circle.

Cyclic/ Inscribed : Nội tiếp Inscribed quadrilateral: Tứ giác nội tiếp

Area of a trapezoid

The area of a trapezoid is basically the average width times the altitude, or as a

formula: 

where

are the lengths of each base

h is the altitude (height)

Trapezoid: A quadrilateral which has at least one pair of parallel sides

Trapezoid: Hình thang Basically: Về cơ bản The average: Trung bình

Area of a regular polygon

1 Given the length of a side.

By definition, all sides of a regular polygon are equal in length If you know the length of one of the

sides, the area is given by the formula: 

Where

a  is the length of any side

n  is the number of sides

tan  is the tangent function calculated in degrees

Regular Polygon: A polygon that has all sides equal and all interior angles equal

Regular polygon: đa giác đều Degrees: Độ

Tangent function: Hàm tiếp tuyến

Area of a regular polygon

2 Given the radius (circumradius)

If you know the radius (distance from the center to a vertex):

r  is the radius (circumradius)

n  is the number of sides

sin  is the sine function calculated in degrees

Area of a regular polygon

3 Given the apothem (inradius)

If you know the apothem, or inradius, (the perpendicular distance from center

to a side.), the area is given by: 

where

a is the length of the apothem (inradius)

n  is the number of sides

tan  is the tangent function calculated in degrees

Apothem: A line segment from the center of a 

regular polygon to the midpoint of a side.

The apothem is also the radius of the  incircle of the polygon

Area

of a circle 

Where:

r: Radius of a circle = 3,14

If you know the diameter

The radius r of a circle is half the diameter d

Substituting r into the area formula 

VOLUME

Volume enclosed by a cube

The volume of a cube have a formula:

where: s  is the length of any edge of the cube.

Cube :A solid with six congruent square faces A regular hexahedron.

Cube: Khối lập phương Volume: Thể tích Edge: Cạnh/ cạnh biên

Volume enclosed by a cylinder

The volume is found by multiplying the area of one end of the cylinder (base) by its

r  is the radius of the circular end of the cylinder

h  height of the cylinder

Volume of a cone

The volume enclosed by a cone is given by the

formula

Where

•  r is the radius of the circular base of the cone

• h is its height

Cone: A solid that has a circular base and a single vertex.

Cone: Hình nón Radius: bán kính

Volume of a pyramid

The volume enclosed by a pyramid is one third of the base area times the perpendicular height As a

formula:

Where:

b is the area of the base of the pyramid

h is its height The height must be measured as the vertical distance from the apex down to the

Volume of a triangular prism

A prism has two congruent, parallel faces called the bases of the prism The volume of any prism can be found by multiplying the area of one of the bases by its height In the case of a triangular prism, each base is a triangle As a formula

V=ah

where:

a is the area of one triangular end face

h is the height

Prism: Lăng trụ Triangular prism: Lăng trụ tam giác Congruent: đồng dạng

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