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Bill is planning the layout of a school playground. For safety reasons he has to mark part of the playground where children cannot play games. A 12m B

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loci playground

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Choose level of difficulty

Loci - Playground

loci playground2

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 1: Draw a sketch of the playground

Loci - Playground

loci playground3

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 2: Sketch the loci of all points 4m from corner D and shade the area within 4m of D

Loci - Playground

loci playground4

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 3: Sketch the loci of all points 3m from the side BC and shade the area within 3m of BC

Loci - Playground

loci playground5

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 4: Calculate the area that is not shaded

Fill in this table

Loci - Playground

loci playground6

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 5: Calculate the largest number of children that can play.

Loci - Playground

End of Problem

Return to Menu

loci playground7

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 1: Sketch a plan of the playground

Loci - Playground

loci playground8

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 2: Sketch the loci of all points 4m from corner D and shade the area within 4m of D

Loci - Playground

loci playground9

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 3: Sketch the loci of all points 3m from the side BC and shade the area within 3m of BC

Loci - Playground

loci playground10

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 4: Calculate the area that is not shaded

Fill in this table

Loci - Playground

loci playground11

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 5: Calculate the largest number of children that can play.

Loci - Playground

End of Problem

Return to Menu

loci playground12

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 1: Draw a sketch

Loci - Playground

loci playground13

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 2: Mark the places where children can’t play.

Loci - Playground

loci playground14

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 3: Calculate the area where children can play

Loci - Playground

loci playground15

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Help

Step 4: Calculate the largest number of children that can play.

Loci - Playground

End of Problem

Return to Menu

loci playground16

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Hint

Draw a sketch.

Loci - Playground

loci playground17

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Hint

Sketch the areas and calculate the area where children can’t play.

Loci - Playground

loci playground18

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Hint

Calculate the largest number of children that can play.

Loci - Playground

End of Problem

Return to Menu

loci playground19

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Hint

Sketch the area where children can’t play

Loci - Playground

loci playground20

Bill is planning the layout of a school playground.

For safety reasons he has to mark part of the playground where children cannot play

games.

A 12m B

10m

D C

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

Children can play games on the rest of the playground.

There has to be at least 1 m2 for each child.

Calculate the largest number of children that can play in the rest of the playground.

Hint

Calculate the largest number of children that can play.

Loci - Playground

End of Problem

Return to Menu