Shape and space: areas

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Shape and space: area & perimeter BTEOTSSBAT: Find the area and perimeter of simple shapes

description

Areas of simple shapes for GCSE mathematics

Transcript of Shape and space: areas

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Shape and space: area & perimeter

BTEOTSSBAT:Find the area and perimeter of simple shapes

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Key wordsDimensionAreaPerimeterHeightLengthWidthCircumferenceParallelogramTrapezium

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Dimensions

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Dimensions

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Dimensions

1 D

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Dimensions

1 D

length

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Dimensions

1 D mmcmmkm

length

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Dimensions

1 D mmcmmkm

length

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Dimensions

1 D

2 D

mmcmmkm

length

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Dimensions

1 D

2 D

mmcmmkm

length

area

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Dimensions

1 D

2 D

mmcmmkm

mm²cm²m²km²

length

area

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Dimensions

1 D

2 D

mmcmmkm

mm²cm²m²km²

length

area

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Dimensions

1 D

2 D

3 D

mmcmmkm

mm²cm²m²km²

length

area

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Dimensions

1 D

2 D

3 D

mmcmmkm

mm²cm²m²km²

length

area

volume

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Dimensions

1 D

2 D

3 D

mmcmmkm

mm²cm²m²km²

mm³cm³m³km³

length

area

volume

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

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

Example

Find the perimeter of this room

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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

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

(a) (b)

6 cm

4 cm

2 cm

4 cm 4 cm

4 cm

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All dimensions in metres

(c) (d)

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

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

The circumference = π diameter or 2 π radius

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

The circumference = π diameter or 2 π radius

Cherry pies delicious

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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

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Shape Area

Rectangle

Triangle

Parallelogram

Trapezium

Circle

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Shape Area

Rectangle Area = height x width

Triangle

Parallelogram

Trapezium

Circle

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Shape Area

Rectangle Area = height x width

TriangleThink of it a half a rectangle

Parallelogram

Trapezium

Circle

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Shape Area

Rectangle Area = height x width

TriangleThink of it a half a rectangle

Area = ½ height x width

Parallelogram

Trapezium

Circle

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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

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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

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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

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WidthH

eigh

tParallelogram

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Hei

ght

Parallelogram Width

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Hei

ght

Parallelogram Width

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Hei

ght

Parallelogram Width

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Hei

ght

Parallelogram Width

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Hei

ght

Parallelogram Width

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Hei

ght

Parallelogram Width

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Hei

ght

Parallelogram Width

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Hei

ght

Parallelogram

Area = height x width!

Width

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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

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

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Hei

ght

Trapeziuma

b

½ (a + b)

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Hei

ght

Trapeziuma

b

½ (a + b)Area = ½ (a + b)x h

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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

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Area = π r²

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Area = π r²

Cherry pies deliciousApple pies are 2

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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

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2. Find the area of the following circles:

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

D = 12 cm D = 24 cm

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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