Mathematics

MATHEMATICS: FORM ONE: Topic 11 – PERIMETERS AND AREAS

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TOPIC 11: PERIMETERS AND AREAS

Perimeters of Triangles and Quadrilaterals

The Perimeters of Triangles and Quadrilaterals

Find the perimeters of triangles and quadrilaterals

Perimeter – is defined as the total length of a closed shape. It is obtained by adding the lengths of the sides inclosing the shape. Perimeter can be measured in , , ,, e. t. c

Examples

Example 1

Find the perimeters of the following shapes

Solution

  1. Perimeter = 7 + 7 + 3 + 3 = 20
  2. Perimeter = 2 + 4 + 5 = 11
  3. Perimeter = 3 + 6 + 4 + 5 + 5 + 4 = 27

Circumference of a Circle

The Value of Pi ( Π)

Estimate the value of Pi ( Π)

The number π is a mathematical constant, the ratio of a circle’s circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter “π” since the mid 18th century, though it is also sometimes spelled out as “pi” (/paɪ/).

The perimeter of a circle is the length of its circumference . = . Experiments show that the ratio of the circumference to the diameter is the same for all circles

The Circumference of a Circle

Calculate the circumference of a circle

Example 2

Find the circumferences of the circles with the following measurements. Take = 3.14

  1. diameter 9
  2. radius 3½
  3. diameter 4.5
  4. radius 8

Solution

Example 3

The circumference of a car wheel is 150 . What is the radius of the wheel?

Solution

Given circumference, = 150

∴ The radius of the wheel is 23.89

Areas of Rectangles and Triangles

The Area of a Rectangle

Calculate the area of a rectangle

Area – can be defined as the total surface covered by a shape. The shape can be rectangle, square, trapezium e. t. c. Area is measured in mm!, cm!,dm!,m! e. t. c

Consider a rectangle of length and width

Consider a square of side

Consider a triangle with a height, ℎ and a base,

Areas of Trapezium and Parallelogram

The Area of a Parallelogram

Calculate area of a parallelogram

A parallelogram consists of two triangles inside. Consider the figure below:

The Area of a Trapezium

Calculate the area of a trapezium

Consider a trapezium of height, ℎ and parallel sides and

Example 4

The area of a trapezium is120 !. Its height is 10 and one of the parallel sides is 4 . What is the other parallel side?

Solution

Given area, = 120 2, height, ℎ = 10 , one parallel side, = 4 . Let other parallel side be,

Then

Area of a Circle

Areas of Circle

Calculate areas of circle

Consider a circle of radius r;

Example 5

Find the areas of the following figures

Solution

Example 6

A circle has a circumference of 30 . What is its area?

Solution

Given circumference, = 30

C = 2

Exercise 1

1. The length of a rectangle is 6 cm, and the width is 4 cm. Find the perimeter and area of a rectangle.

2. Find the area of a circle with diameter 35 cm.( use Π = 22/7)

3. Calculate the area of a trapezium with parallel sides 3 cm and 5 cm and distance between them is 12 cm.

4. Find the height of a triangle with base 50 cm and area 300 cm2.

5. Find the area of a circle of diameter 40 cm. ( given π=3.14).

TOPIC 11: PERIMETERS AND AREAS

Perimeters of Triangles and Quadrilaterals

The Perimeters of Triangles and Quadrilaterals

Find the perimeters of triangles and quadrilaterals

Perimeter – is defined as the total length of a closed shape. It is obtained by adding the lengths of the sides inclosing the shape. Perimeter can be measured in , , ,, e. t. c

Examples

Example 1

Find the perimeters of the following shapes

Solution

  1. Perimeter = 7 + 7 + 3 + 3 = 20
  2. Perimeter = 2 + 4 + 5 = 11
  3. Perimeter = 3 + 6 + 4 + 5 + 5 + 4 = 27

Circumference of a Circle

The Value of Pi ( Π)

Estimate the value of Pi ( Π)

The number π is a mathematical constant, the ratio of a circle’s circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter “π” since the mid 18th century, though it is also sometimes spelled out as “pi” (/paɪ/).

The perimeter of a circle is the length of its circumference . = . Experiments show that the ratio of the circumference to the diameter is the same for all circles

The Circumference of a Circle

Calculate the circumference of a circle

Example 2

Find the circumferences of the circles with the following measurements. Take = 3.14

  1. diameter 9
  2. radius 3½
  3. diameter 4.5
  4. radius 8

Solution

Example 3

The circumference of a car wheel is 150 . What is the radius of the wheel?

Solution

Given circumference, = 150

∴ The radius of the wheel is 23.89

Areas of Rectangles and Triangles

The Area of a Rectangle

Calculate the area of a rectangle

Area – can be defined as the total surface covered by a shape. The shape can be rectangle, square, trapezium e. t. c. Area is measured in mm!, cm!,dm!,m! e. t. c

Consider a rectangle of length and width

Consider a square of side

Consider a triangle with a height, ℎ and a base,

Areas of Trapezium and Parallelogram

The Area of a Parallelogram

Calculate area of a parallelogram

A parallelogram consists of two triangles inside. Consider the figure below:

The Area of a Trapezium

Calculate the area of a trapezium

Consider a trapezium of height, ℎ and parallel sides and

Example 4

The area of a trapezium is120 !. Its height is 10 and one of the parallel sides is 4 . What is the other parallel side?

Solution

Given area, = 120 2, height, ℎ = 10 , one parallel side, = 4 . Let other parallel side be,

Then

Area of a Circle

Areas of Circle

Calculate areas of circle

Consider a circle of radius r;

Example 5

Find the areas of the following figures

Solution

Example 6

A circle has a circumference of 30 . What is its area?

Solution

Given circumference, = 30

C = 2

Exercise 1

1. The length of a rectangle is 6 cm, and the width is 4 cm. Find the perimeter and area of a rectangle.

2. Find the area of a circle with diameter 35 cm.( use Π = 22/7)

3. Calculate the area of a trapezium with parallel sides 3 cm and 5 cm and distance between them is 12 cm.

4. Find the height of a triangle with base 50 cm and area 300 cm2.

5. Find the area of a circle of diameter 40 cm. ( given π=3.14).

TOPIC 11: PERIMETERS AND AREAS

Perimeters of Triangles and Quadrilaterals

The Perimeters of Triangles and Quadrilaterals

Find the perimeters of triangles and quadrilaterals

Perimeter – is defined as the total length of a closed shape. It is obtained by adding the lengths of the sides inclosing the shape. Perimeter can be measured in , , ,, e. t. c

Examples

Example 1

Find the perimeters of the following shapes

Solution

  1. Perimeter = 7 + 7 + 3 + 3 = 20
  2. Perimeter = 2 + 4 + 5 = 11
  3. Perimeter = 3 + 6 + 4 + 5 + 5 + 4 = 27

Circumference of a Circle

The Value of Pi ( Π)

Estimate the value of Pi ( Π)

The number π is a mathematical constant, the ratio of a circle’s circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter “π” since the mid 18th century, though it is also sometimes spelled out as “pi” (/paɪ/).

The perimeter of a circle is the length of its circumference . = . Experiments show that the ratio of the circumference to the diameter is the same for all circles

The Circumference of a Circle

Calculate the circumference of a circle

Example 2

Find the circumferences of the circles with the following measurements. Take = 3.14

  1. diameter 9
  2. radius 3½
  3. diameter 4.5
  4. radius 8

Solution

Example 3

The circumference of a car wheel is 150 . What is the radius of the wheel?

Solution

Given circumference, = 150

∴ The radius of the wheel is 23.89

Areas of Rectangles and Triangles

The Area of a Rectangle

Calculate the area of a rectangle

Area – can be defined as the total surface covered by a shape. The shape can be rectangle, square, trapezium e. t. c. Area is measured in mm!, cm!,dm!,m! e. t. c

Consider a rectangle of length and width

Consider a square of side

Consider a triangle with a height, ℎ and a base,

Areas of Trapezium and Parallelogram

The Area of a Parallelogram

Calculate area of a parallelogram

A parallelogram consists of two triangles inside. Consider the figure below:

The Area of a Trapezium

Calculate the area of a trapezium

Consider a trapezium of height, ℎ and parallel sides and

Example 4

The area of a trapezium is120 !. Its height is 10 and one of the parallel sides is 4 . What is the other parallel side?

Solution

Given area, = 120 2, height, ℎ = 10 , one parallel side, = 4 . Let other parallel side be,

Then

Area of a Circle

Areas of Circle

Calculate areas of circle

Consider a circle of radius r;

Example 5

Find the areas of the following figures

Solution

Example 6

A circle has a circumference of 30 . What is its area?

Solution

Given circumference, = 30

C = 2

Exercise 1

1. The length of a rectangle is 6 cm, and the width is 4 cm. Find the perimeter and area of a rectangle.

2. Find the area of a circle with diameter 35 cm.( use Π = 22/7)

3. Calculate the area of a trapezium with parallel sides 3 cm and 5 cm and distance between them is 12 cm.

4. Find the height of a triangle with base 50 cm and area 300 cm2.

5. Find the area of a circle of diameter 40 cm. ( given π=3.14).

TOPIC 11: PERIMETERS AND AREAS

Perimeters of Triangles and Quadrilaterals

The Perimeters of Triangles and Quadrilaterals

Find the perimeters of triangles and quadrilaterals

Perimeter – is defined as the total length of a closed shape. It is obtained by adding the lengths of the sides inclosing the shape. Perimeter can be measured in , , ,, e. t. c

Examples

Example 1

Find the perimeters of the following shapes

Solution

  1. Perimeter = 7 + 7 + 3 + 3 = 20
  2. Perimeter = 2 + 4 + 5 = 11
  3. Perimeter = 3 + 6 + 4 + 5 + 5 + 4 = 27

Circumference of a Circle

The Value of Pi ( Π)

Estimate the value of Pi ( Π)

The number π is a mathematical constant, the ratio of a circle’s circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter “π” since the mid 18th century, though it is also sometimes spelled out as “pi” (/paɪ/).

The perimeter of a circle is the length of its circumference . = . Experiments show that the ratio of the circumference to the diameter is the same for all circles

The Circumference of a Circle

Calculate the circumference of a circle

Example 2

Find the circumferences of the circles with the following measurements. Take = 3.14

  1. diameter 9
  2. radius 3½
  3. diameter 4.5
  4. radius 8

Solution

Example 3

The circumference of a car wheel is 150 . What is the radius of the wheel?

Solution

Given circumference, = 150

∴ The radius of the wheel is 23.89

Areas of Rectangles and Triangles

The Area of a Rectangle

Calculate the area of a rectangle

Area – can be defined as the total surface covered by a shape. The shape can be rectangle, square, trapezium e. t. c. Area is measured in mm!, cm!,dm!,m! e. t. c

Consider a rectangle of length and width

Consider a square of side

Consider a triangle with a height, ℎ and a base,

Areas of Trapezium and Parallelogram

The Area of a Parallelogram

Calculate area of a parallelogram

A parallelogram consists of two triangles inside. Consider the figure below:

The Area of a Trapezium

Calculate the area of a trapezium

Consider a trapezium of height, ℎ and parallel sides and

Example 4

The area of a trapezium is120 !. Its height is 10 and one of the parallel sides is 4 . What is the other parallel side?

Solution

Given area, = 120 2, height, ℎ = 10 , one parallel side, = 4 . Let other parallel side be,

Then

Area of a Circle

Areas of Circle

Calculate areas of circle

Consider a circle of radius r;

Example 5

Find the areas of the following figures

Solution

Example 6

A circle has a circumference of 30 . What is its area?

Solution

Given circumference, = 30

C = 2

Exercise 1

1. The length of a rectangle is 6 cm, and the width is 4 cm. Find the perimeter and area of a rectangle.

2. Find the area of a circle with diameter 35 cm.( use Π = 22/7)

3. Calculate the area of a trapezium with parallel sides 3 cm and 5 cm and distance between them is 12 cm.

4. Find the height of a triangle with base 50 cm and area 300 cm2.

5. Find the area of a circle of diameter 40 cm. ( given π=3.14).

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