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Mixed exercises
{{exercise_number}}. Using quad paper, draw a rectangle with \latex{ 9 } and \latex{ 4 } units long sides. Divide the rectangle along the lines of the quad paper into two congruent parts to form a square.
{{exercise_number}}. In the pentomino game, the following polygons with an area of \latex{ 5 } units have to be placed on an \latex{ 8\times8 } chess board so that they do not cover each other. How many polygons with different perimeters are there in pentomino?
\latex{ T }
\latex{ I }
\latex{ X }
\latex{ V }
\latex{ P }
\latex{ U }
\latex{ Z }
\latex{ F }
\latex{ Y }
\latex{ W }
\latex{ L }
\latex{ N }
{{exercise_number}}. TETRIS is played with seven polygons. The perimeter of which one is different?
g)
a)
b)
c)
d)
e)
f)
{{exercise_number}}. In which word is the perimeter of the letters the largest? The area of which word is the smallest?
b)
a)
{{exercise_number}}. The perimeter of all the rectangles in the image is \latex{ 24 } units. Which rectangle has the greatest area?
\latex{F }
\latex{ A }
\latex{B }
\latex{C }
\latex{D }
\latex{E }
{{exercise_number}}. Determine which of the following polygons has the largest perimeter without measuring them.
\latex{ E }
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
{{exercise_number}}. How many rectangles can be made using a) \latex{ 12 }; b) \latex{ 16 }; c) \latex{ 36 } squares with \latex{ 1 } \latex{ cm } long sides? Which one has the largest and which one has the smallest perimeter? Make a table.
{{exercise_number}}. How many rectangles are there whose perimeter is \latex{ 16 } units and the length of the sides is a whole number? Which one has the largest, and which one has the smallest area?
{{exercise_number}}. How many rectangles with an area of \latex{ 24 } \latex{ cm^{2} } are there? (The sides in \latex{ centimetres } are whole numbers.) What is the perimeter of these rectangles?
{{exercise_number}}. The sides of the polygons in the image are \latex{ 1 } \latex{ cm } long, and the adjacent sides are perpendicular to each other. What is the perimeter and the area of each polygon? Determine the rule and draw the next two polygons in the sequence.
\latex{ D }
\latex{ A }
\latex{ B }
\latex{ C }
{{exercise_number}}. When flooring a rectangular room, \latex{ 19 } \latex{ metres } of skirting was used. No skirting was used for the \latex{ 1 } \latex{ m } wide door. One of the sides of the room is \latex{ 2 } \latex{ m } longer than the other. What was the area of the room?
{{exercise_number}}. What is the area of a rectangular carpet if one side is \latex{ 2 } \latex{ m } long and its perimeter is \latex{ 10 } \latex{ m ?} How much does the cleaning cost if the carpet cleaner charges €\latex{ 2 } per \latex{ 1 } \latex{ m^{2} ?}
{{exercise_number}}. The perimeter of a rectangle is \latex{ 1 } \latex{ cm }, and one of its sides is \latex{\frac{1}{3}} \latex{ cm } longer than the other. What is the area of the rectangle?
{{exercise_number}}. What is the area of a rectangular room if its perimeter is \latex{ 15 } \latex{ m } and one side is one \latex{ metre } and a half shorter than the other?
{{exercise_number}}. Rectangular cards are hung on a square-shaped board whose sides are \latex{ 10 } units long. The cards do not overlap or go over the edge of the board. How many rectangular cards can be placed on the board if the sides of the cards are
a) \latex{ 2 } and \latex{ 3 } units;
b) \latex{ 4 } and \latex{ 6 } units;
c) \latex{ 5 } and \latex{ 6 } units?
{{exercise_number}}. What is the area of the red parts if one small square is one unit?
Help:
Divide the red
figures into
triangles and
rectangles along
the lines, or
subtract the sum
of the yellow
parts from the
entire area.
Divide the red
figures into
triangles and
rectangles along
the lines, or
subtract the sum
of the yellow
parts from the
entire area.
h)
e)
f)
g)
a)
b)
c)
d)
{{exercise_number}}. The table shows the dimensions of the playing fields of some team sports. (→)
a) Arrange them in ascending order according to their perimeter.
b) Arrange them in ascending order according to their area.
b) Arrange them in ascending order according to their area.
Length in
\latex{metres}
\latex{ 31 } \latex{\frac{1}{2}}
Width in
\latex{metres}
Sport
ice hockey
handball
basketball
football
volleyball
water polo
\latex{ 18 }
\latex{ 27 }
\latex{ 18 }
\latex{ 9 }
\latex{ 70 }
\latex{ 105 }
\latex{ 28 }
\latex{ 15 }
\latex{ 20 }
\latex{ 40 }
\latex{ 61 }
{{exercise_number}}. How much does the perimeter of a square with \latex{ 5 } \latex{ cm } sides increase if each side is
a) increased by \latex{ 3 } \latex{ centimetres };
b) increased by \latex{ 10 } \latex{ centimetres };
c) doubled;
d) tripled?
How does the perimeter change? Make a drawing as well.
{{exercise_number}}. \latex{ 5 } squares were made using \latex{ 16 } matchsticks. Move two matchsticks to make four congruent squares. (→)
(You cannot place matchsticks on top of each other; each matchstick has to be the side of a square.)
