Circumference And Area

MATHEMATICS 8 UNIT 10 PERIMETER PERIMETER OF POLYGONS CIRCUMFERENCE OF A CIRCLE AREAS OF RECTANGLES AND SQUARES AREA OF A PARALLELOGRAM AREA OF A TRIANGLE AREA OF A CIRCLE

PERIMETER A PERIMETER IS THE DISTANCE AROUND AN OBJECT. IT IS THE SUM OF THE LENGTH OF ALL SIDES

4

4

3 4 6

Perimeter is equal to the sum of all sides. P=4+4+4+6+3 P = 21

Perimeter of a Rectangle 5 2

2 5 P = 2L + 2W P=2x5+2x2 P = 10 + 4 P = 14

A rectangle is a type of quadrilateral where opposite sides are equal in length. To find the perimeter, we can use the formula

P = 2 x length + 2 x width or P = 2L + 2W

Perimeter of a Regular Polygon A regular polygon is a multi-sided figure where all sides are equal.

3

3

3

3 3

In this regular pentagon, all five sides are equal. P=5xs

P=5xs P=5x3 P = 15

CIRCUMFERENCE OF A CIRCLE The circumference of circle is the measurement of the distance around. The diameter of a circle is the length of a line that runs through the centre point of a circle and touches two different parts of the circumference.

Diameter

Circumference

Circumference If you were to measure the circumference of any circle, then divide it by the diameter, you would arrive at the same answer. This answer is called a constant and, in the case of circles is called pi.

The symbol for pi is the Greek letter B

Circumference Since B is a constant, we can use it to calculate the circumference of a circle when we are given the diameter. The circumference of a circle is equal to the diameter multiplied by pi 12 cm

C=Bxd C = Bd C = 3.14 x 12 cm C= 37.68 cm

The radius of a circle is the measurement from its centre point to its circumference. The radius, therefore, is half the measure of the diameter.

D = 2 x r or D = 2r

We can calculate the circumference of a circle if we know the radius. C=Bxd C=Bx2xr C = B2r

4 cm C = 2Br C = 2 x 3.14 x 4 C = 6.28 x 4 C = 25.12 cm

AREA OF A RECTANGLE AND SQUARE AREA IS THE NUMBER OF SQUARE UNITS NEEDED TO COVER A SURFACE

4 cm

4 cm

4 cm

4 cm

If you count the number of blocks, you can see that the surface area of the patio is covered by 16 of them. You can also calculate the area of this figure by using the following formula:

A = length x width A = 4 cm x 4 cm A = 16 cm 2

10 cm 3 cm

AREA = LENGTH x WIDTH

2

AREA OF A PARALLELOGRAM A PARALLELOGRAM IS A FOUR SIDED FIGURE WHERE OPPOSITE SIDES ARE EQUAL AND PARALLEL

> 3.5 cm

>

base 7 cm

height

Area of a Parallelogram A = base x height A = 7 cm x 3.5 cm

A = 24.5 cm

2

AREA OF A TRIANGLE A

D

B

C This formula can also be written as

A=½bxh

BD divides parallelogram ABCD into two equal triangles. We know the area of a parellogram is: A=bxh Therefore, if we divide the parallelogram into two triangles, the formula for the area of a triangle is:

A=bxh 2

AREA OF A CIRCLE 2

3.8 cm 2

2

7.6 cm

Diameter = 7.6 cm Radius = 3.8 cm