Shape and space: areas

Shape and space: area & perimeter

BTEOTSSBAT:Find the area and perimeter of simple shapes

Key wordsDimensionAreaPerimeterHeightLengthWidthCircumferenceParallelogramTrapezium

Dimensions

Dimensions

Dimensions

1 D

Dimensions

1 D

length

Dimensions

1 D mmcmmkm

length

Dimensions

1 D mmcmmkm

length

Dimensions

1 D

2 D

mmcmmkm

length

Dimensions

1 D

2 D

mmcmmkm

length

area

Dimensions

1 D

2 D

mmcmmkm

mm²cm²m²km²

length

area

Dimensions

1 D

2 D

mmcmmkm

mm²cm²m²km²

length

area

Dimensions

1 D

2 D

3 D

mmcmmkm

mm²cm²m²km²

length

area

Dimensions

1 D

2 D

3 D

mmcmmkm

mm²cm²m²km²

length

area

volume

Dimensions

1 D

2 D

3 D

mmcmmkm

mm²cm²m²km²

mm³cm³m³km³

length

area

volume

PerimeterThe perimeter of a shape is the distance around its edges.

PerimeterThe perimeter of a shape is the distance around its edges.

Example

Find the perimeter of this room

To find the perimeter we need to know the lengths of some of the missing sides. The side joining shapes (a) and (b) is 7 in total, but 3 is missing from it so it has a length of 7 -3 = 4.The total perimeter will be:shape (a) 7 + 7 + 7 + 4 = 25shape (b) 3 + 3 +3 = 9total = 25 + 9 = 34 units.

PerimeterThe perimeter of a shape is the distance around its edges.

Example

Find the perimeter of this room

Now try these 1Find the perimeter of the following shapes:

(a) (b)

6 cm

4 cm

2 cm

4 cm 4 cm

4 cm

All dimensions in metres

(c) (d)

The perimeter of a circleThe perimeter of a circle is called the circumference.

The perimeter of a circleThe perimeter of a circle is called the circumference.

The circumference = π diameter or 2 π radius

The perimeter of a circleThe perimeter of a circle is called the circumference.

The circumference = π diameter or 2 π radius

Cherry pies delicious

The perimeter of a circleThe perimeter of a circle is called the circumference.

2 cm 10 cm 1 m

The circumference = π diameter or 2 π radius

Find the circumference of these circles

Shape Area

Rectangle

Triangle

Parallelogram

Trapezium

Circle

Shape Area

Rectangle Area = height x width

Triangle

Parallelogram

Trapezium

Circle

Shape Area

Rectangle Area = height x width

TriangleThink of it a half a rectangle

Parallelogram

Trapezium

Circle

Shape Area

Rectangle Area = height x width

TriangleThink of it a half a rectangle

Area = ½ height x width

Parallelogram

Trapezium

Circle

Shape Area

Rectangle Area = height x width

TriangleThink of it a half a rectangle

Area = ½ height x width = ½ base x perpendicular height

Parallelogram

Trapezium

Circle

Now try these 2

1. Find the area of these triangles:

5.2 cm

6.1 cm

5 cm

4 cm

5 cm

4 cm

3 cm

Shape Area

Rectangle Area = height x width

TriangleThink of it a half a rectangle

Area = ½ height x width = ½ base x perpendicular height

Parallelogram

Trapezium

Circle

WidthH

eigh

tParallelogram

Hei

ght

Parallelogram Width

Hei

ght

Parallelogram Width

Hei

ght

Parallelogram Width

Hei

ght

Parallelogram Width

Hei

ght

Parallelogram Width

Hei

ght

Parallelogram Width

Hei

ght

Parallelogram Width

Hei

ght

Parallelogram

Area = height x width!

Width

Shape Area

Rectangle Area = height x width

Triangle Area = ½ height x width = ½ base x perpendicular height

Parallelogram Area = height x width

Trapezium

Circle

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

Hei

ght

Trapeziuma

b

½ (a + b)

Hei

ght

Trapeziuma

b

½ (a + b)Area = ½ (a + b)x h

Shape Area

Rectangle Area = height x width

Triangle Area = ½ height x width = ½ base x perpendicular height

Parallelogram Area = height x width

Trapezium Area = ½ (a+b) x perpendicular height

Circle

Area = π r²

Area = π r²

Cherry pies deliciousApple pies are 2

Shape Area

Rectangle Area = height x width

Triangle Area = ½ height x width = ½ base x perpendicular height

Parallelogram Area = height x width

Trapezium Area = ½ (a+b) x perpendicular height

CircleArea = π r²

2. Find the area of the following circles:

r = 4 cm r = 2.5 cm r = 3 cm

D = 12 cm D = 24 cm

3. Find the area of the following shapes:

5 cm 12 cm

4 cm4 cm

4 cm

4 cm 10 cm

3 cm

8 cm

3 cm

10 cm