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
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
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
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
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
Help
Step 4:
Calculate the area
that is not shaded
Fill in this table
10m
Shape
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.
Playground
Within 4m of D
Within 3m of BC
Play Area
Area
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
Help
Step 5:
Calculate the largest
number of children
that can play.
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.
End of Problem
Return to Menu
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.
Help
Step 1:
Sketch a plan of
the playground
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.
Help
Step 2:
Sketch the loci of all
points 4m from
corner D and shade
the area within 4m
of D
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.
Help
Step 3:
Sketch the loci of all
points 3m from
the side BC and
shade the area
within 3m of BC
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
Help
Step 4:
Calculate the area
that is not shaded
Fill in this table
10m
Shape
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.
Playground
Within 4m of D
Within 3m of BC
Play Area
Area
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
Help
Step 5:
Calculate the largest
number of children
that can play.
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.
End of Problem
Return to Menu
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.
Help
Step 1:
Draw a sketch
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.
Help
Step 2:
Mark the places
where children can’t
play.
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.
Help
Step 3:
Calculate the area
where children can
play
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
Help
Step 4:
Calculate the largest
number of children
that can play.
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.
End of Problem
Return to Menu
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.
Hint
Draw a sketch.
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.
Hint
Sketch the areas and calculate
the area where children can’t
play.
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
Hint
Calculate the largest number
of children that can play.
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.
End of Problem
Return to Menu
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.
Hint
Sketch the area where
children can’t play
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
Hint
Calculate the largest number
of children that can play.
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.
End of Problem
Return to Menu