ID 697

Geometry and  Measurement K9A hall is cube-shaped.
The volume of the hall is 216 cubic meters.
The door is 3 meters high.

Find the length of a side of the floor.



ID 702

Geometry and  Measurement K9Which shape could NOT be a cross section of a cone?



ID 703

Geometry and  Measurement K9What is the shortest path?



ID 704

Geometry and  Measurement K9The aquarium was full of water.
A girl has tipped it on its side,
so five liters are left.

How much water does the aquarium hold when it is full of water.



ID 706

Geometry and  Measurement K9Which fraction of this triangle is shaded?



ID 707

Geometry and  Measurement K9One face of a rectangular box has an area of 15 square cm. Another face is 20 square cm and the other face is 12 square cm.

What is the height of the box?



ID 708

Geometry and  Measurement K9Find the length of the side of a cube whose volume is numerically the same as its surface area.



ID 709

Geometry and  Measurement K9This large cube is made from smaller wooden cubes.
All of the faces of the large cube are painted blue, and then it is taken apart.

What fraction of the surface is blue?



ID 713

Geometry and  Measurement K9A rectangular floor measures 3 meters by 9 meters.
It is tiled with one-square meter tiles.

Through how many tiles would the diagonal line in this rectangle pass?



ID 714

Geometry and  Measurement K9A sports club is replacing its water supply lines for a swimming pool. The current system uses two pipes, A and B, which have circular cross-sections with diameters of 6 and 8 cm, respectively. The club decides to use a single replacement pipe with the same capacity.

What is the diameter of the new pipe?



ID 715

Geometry and  Measurement K9John is building a flight of stairs.
Each stair is the same size.

What is the height of the flight of stairs X?



ID 717

Geometry and  Measurement K9Three corners of a square are A(1,4), B(4,6), and C(6,3).

Where is the fourth corner D?



ID 720

Geometry and  Measurement K9How many red circles can be placed inside the blue circle without intersecting?



ID 721

Geometry and  Measurement K9Members of the Green Tennis Club are creating a logo.
The logo of the club is a blue square with a green shape inside.

What percentage of the logo is blue?



ID 722

Geometry and  Measurement K9Mr. Clever gave his students this pattern of gray tiles.

Develop an equation to represent the number of gray tiles, t, for any size of the inner square, n.



ID 724

Geometry and  Measurement K9Which side of this shape is 5 units long?



ID 731

Geometry and  Measurement K9A wheel with a red mark on it is rolled along a straight line.

What is the path the mark follows during one revolution?



ID 734

Geometry and  Measurement K9The squares have side lengths of 2 and 4.

Find the area of the colored region.



ID 736

Geometry and  Measurement K9The figure consists of congruent squares.
The perimeter of the figure is 10 meters.

What is the area of the figure?



ID 739

Geometry and  Measurement K9The figure shows a regular octagon.

What is the area of the colored part as a fraction of the area of the entire octagon?



ID 750

Geometry and  Measurement K9I want to build a fence around a rectangular garden.
The garden has an area of 100 square meters.

The fence posts must be placed 1 meter apart.

What is the minimum and maximum number of fence posts needed?



ID 755

Geometry and  Measurement K9How many planes of symmetry does an Egyptian pyramid have?



ID 760

Geometry and  Measurement K9Find the line that splits the area of the ten squares into two equal parts.

AB = BC



ID 768

Geometry and  Measurement K9The bigger star is similar to the smaller one.
It is twice the height of the smaller star.

How much greater is its area?



ID 769

Geometry and  Measurement K9How many circles can be placed inside the square without intersecting each other?



ID 774

Geometry and  Measurement K9The area of the smallest square is 124 square meters.

What is the area of the biggest square?



ID 775

Geometry and  Measurement K9Cut 1 cube into 8 pieces. One of the pieces is a cube whose volume is three times less than that of the original cube.

What is the percentage of new surface area compared with the original cube's surface area?



ID 1005

Geometry and  Measurement K9Find two pairs of shapes that are exactly the same distance apart, where the distance between two shapes is defined as the distance between their centers.



ID 1021

Geometry and  Measurement K9You are at point A.
You can only walk to the north or east.
For example, you can go to point B by two different ways.

How many different ways are there to reach point C?



ID 1038

Geometry and  Measurement K9For which capital letter of the English alphabet would you use the greatest amount of paint?



ID 1046

Geometry and  Measurement K9The arrow top is at the midpoint of the edge of the rectangle.
What fraction of the rectangle is shaded?



ID 1072

Geometry and  Measurement K9Each diagonal of a cube is increased by 50%.

What was the percentage increase of the volume of the cube?



ID 1082

Geometry and  Measurement K9A and B are midpoints of the corresponding sides of the rectangle.

What fraction of the rectangle is the green part?



ID 1251

Geometry and  Measurement K9 Every face of a cube has at least one white edge.

What is the smallest number of white edges?



ID 1260

Geometry and  Measurement K9A circle is inscribed in trapezoid.

What is the minimum possible perimeter of the trapezoid?



ID 1265

Geometry and  Measurement K9The circumference of each circle is 24 meters.

What is the perimeter of the red region?



ID 1373

Geometry and  Measurement K9 John cuts a large piece of cheese into small pieces using straight cuts from a very sharp cheese wire.
He does not move the pieces from the original shape while he cuts the cheese.

How many rectangular pieces of cheese can he get using only five cuts?



ID 1393

Geometry and  Measurement K9All triangles are inscribed in circles with a diameter of 1 meter.

Find the triangle with the largest area.



ID 1397

Geometry and  Measurement K9What is the sum of the marked angles?



ID 1461

Geometry and  Measurement K9Four touching circles have the same radiuses.

Their centers are the corners of what shape?



ID 1474

Geometry and  Measurement K9Two polygons are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.

In how many ways can a regular hexagon be divided by a straight line into two congruent pentagons?



ID 1478

Geometry and  Measurement K9Which of the following could be the graph showing the area Y of a square with the side length X?



ID 1482

Geometry and  Measurement K9Fifteen billiard balls perfectly fit into a triangular rack.
What is the largest number of the balls that fit into the rack when its side lengths are increased by 20%?



ID 1551

Geometry and  Measurement K9 I want to cut round bread into eight equal pieces.

What is the smallest number of straight cuts I can make to achieve this?



ID 1567

Geometry and  Measurement K9The diagram shows my square pond with a tree in each corner.

How much can I increase its area if I transform it into a right-angled triangle pond and keep the trees in the same place?



ID 1583

Geometry and  Measurement K9How many colored four-unit shapes can be placed inside the 6x6 square without intersecting each other?

You may turn the shape.
Find the greatest number.



ID 1595

Geometry and  Measurement K9A solid is a cube with three tunnels drilled through it, as you can see in the picture.

How many blocks are there in the solid?



ID 1599

Geometry and  Measurement K9Four matchsticks form a square.

How many non-overlapping squares can be formed using seven matchsticks?



ID 1756

Geometry and  Measurement K9Ten acrobats are evenly spaced at a circus circular arena.

Which acrobat is directly opposite the ninth performer?



ID 1792

Geometry and  Measurement K9It costs $24 to paint a cube.
Before painting, it was cut into eight cubes.

What is the cost to paint these small cubes?



ID 1793

Geometry and  Measurement K9Six shapes can be fitted together with no gaps and no overlaps to form a rectangle.

What is the smallest dimension of the rectangle?



ID 1803

Geometry and  Measurement K9I want to cut this shape into four pieces all of precisely the same size and shape.

Which is such a piece?



ID 1808

Geometry and  Measurement K9What is the greatest number of possible points of intersection of three circles?



ID 1812

Geometry and  Measurement K9A rectangle floor 12 x 16 is covered by square tiles of sides 40 cm.
A chalk line is drawn from one corner to the diagonally opposite corner.
How many tiles have a chalk line segment on them?



ID 1838

Geometry and  Measurement K9The picture shows a regular pentagon and an equilateral triangle.

How large is the marked angle?



ID 1847

Geometry and  Measurement K9The colored figure in the picture consists of identical isosceles right triangles.

What is the area of the blue shape?



ID 1849

Geometry and  Measurement K9How many inner right angles are possible in a hexagon?



ID 1868

Geometry and  Measurement K9A guard walks completely around the walls of a rectangular castle with a perimeter of 10 km.
From any point on his path, he can see exactly 1 km horizontally in all directions, except the wall.

What is the area of the region that contains all points that the guard can see during his walk?



ID 1924

Geometry and  Measurement K9In a triangle, the sum of two of the angles is equal to the third, and the lengths of the two longer sides are 17 and 15.

What is the length of the shortest side?



ID 1938

Geometry and  Measurement K9If the coordinates of one end point of a line segment are (1 , 2 , -3) and the coordinates of the midpoint are (-3 , 2, 1), what are the coordinates of the other endpoint?



ID 1951

Geometry and  Measurement K9What is the probability that a point chosen randomly from the interior of a rectangle is closer to the rectangle's center than it is to any of the rectangle's vertices?



ID 1976

Geometry and  Measurement K9Eight poles are evenly spaced on the circumference of a big circle.
What is the largest number of ropes that can be stretched between two poles so that no two ropes intersect at any point?



ID 1993

Geometry and  Measurement K9A quadrilateral with one pair of parallel sides is referred to as a trapezoid.

A trapezoid has perpendicular diagonals of lengths 4 and 6.

What is the area of the trapezoid?



ID 2043

Geometry and  Measurement K9Find the sum of the five marked angles of a star that is inscribed into a circle.



ID 2208

Geometry and  Measurement K9Find the angle between two diagonals drawn on two faces of the cube.



ID 2280

Geometry and  Measurement K9Which red piece can be put with the blue one to form a rectangle?



ID 2288

Geometry and  Measurement K9What is the area of the square?



ID 2290

Geometry and  Measurement K9A clock says that the time is 14:20.
The minute hand moves 300 degrees.

How many degrees has the hour hand turned?



ID 3009

Geometry and  Measurement K9Identify two shapes with the same perimeter.



ID 3010

Geometry and  Measurement K9What is the perimeter of the triangle?



ID 3016

Geometry and  Measurement K9If each edge length of this shape is tripled, what will happen to its volume?



ID 3017

Geometry and  Measurement K9A curtain covers a window as shown on the right.
We approximate the area of the curtain by 2 triangles.
The window is 24 by 36 inches.
How much of the window area is covered by the curtain?



ID 3023

Geometry and  Measurement K9Which angle is largest?



ID 3025

Geometry and  Measurement K9Which shape is closer to the point (0,0) ?



ID 3030

Geometry and  Measurement K9How many right angles are possible in a polygon with six sides (hexagon)?



ID 3031

Geometry and  Measurement K9Which triangle has angles that appear to measure 42°, 48° and 90°?



ID 3032

Geometry and  Measurement K9Which figure can be rotated 72° about its center and have its final orientation appear the same as the original orientation?



ID 3033

Geometry and  Measurement K9Find the shape

that has more than 5 sides and
no right angles ( 90°).



ID 3034

Geometry and  Measurement K9In the diagram, the radii of the two concentric circles are 4.5 and 10, respectively.

What fraction of the bigger circle is shaded?



ID 3035

Geometry and  Measurement K9If two sides of the triangle have lengths of 22 and 33, which of the following could be the perimeter of the triangle?



ID 3036

Geometry and  Measurement K9Which shape has the largest white region in terms of area?



ID 3041

Geometry and  Measurement K9If G is the total area of the green regular octagon and R is the total area of the red regular octagon, which is correct?



ID 3078

Geometry and  Measurement K9Find the area of the triangle ABC



ID 3088

Geometry and  Measurement K9The figure shows a regular octagon.

What is the area of the colored part as a fraction of the area of the entire octagon?



ID 3102

Geometry and  Measurement K9Estimate the size of the square if the circle diameter is 25 inches.



ID 3107

Geometry and  Measurement K9The area of the smallest square is 12 square inches.

What is the area of the largest square?



ID 3116

Geometry and  Measurement K9Which is the plan view of the 3-D shape?



ID 3120

Geometry and  Measurement K9Which two lines are perpendicular?



ID 3121

Geometry and  Measurement K9What is the volume of the figure, if X = 4?



ID 3135

Geometry and  Measurement K9In a triangle, the sum of two of the angles is equal to the third.
The lengths of the sides are 12,13 and X.

Find X.



ID 3193

Geometry and  Measurement K9The blocks of ice are of the same height.

Which assembly melts slowest?



ID 3212

Geometry and  Measurement K9A telephone company places round cables in round ducts.

What position of the cables is the worst and demands using the round duct with the larger diameter?



ID 3298

Geometry and  Measurement K9What is the area of a square with a diagonal of length 10 units?



ID 3357

Geometry and  Measurement K9Eugenia discovered round ink spots on her music paper.

Which music paper has smaller amount of ink?



ID 3390

Geometry and  Measurement K9Anna takes a rope that is 24 ft long and creates a square.
Bob takes the rope and creates a rectangle that has an area 75% of the square's area.

What is the length of the rectangle?



ID 3663

Geometry and  Measurement K9Which shape cannot be formed by the intersection of two squares?



ID 3688

Geometry and  Measurement K9Which is the odd one out?



ID 3716

Geometry and  Measurement K9Cut the shape into two pieces and create a square from them.

How many small squares are in the smaller of these two shapes?



ID 3770

Geometry and  Measurement K9What is the absolute difference between the largest and smallest possible areas of two rectangles that each has a perimeter of 100 units and integer side lengths?



ID 3782

Geometry and  Measurement K9Three equilateral triangles form seven unique regions.

What is the maximum number of regions that can be formed by three congruent, overlapping triangles?



ID 3936

Geometry and  Measurement K9I increase the cube so that the diagonal AB doubles its original size.

How many times does the volume increase?



ID 3990

Geometry and  Measurement K9All three pathways consist of semi-circles. 

Which pathway from A to B is the shortest?



ID 4017

Geometry and  Measurement K9I have a cube with a volume of 1000 cm3.
I make the length 20% longer, the width 10% shorter and the height 10% shorter.

What is the new volume?



ID 4080

Geometry and  Measurement K9Find the maximum area of a rectangle that has a perimeter of 36 m.



ID 4333

Geometry and  Measurement K9If we add all these vectors and place the start of the resulting vector at the origin, where does the resulting vector end?



ID 4485

Geometry and  Measurement K9What is the ratio of the reverse area of a dime to its circumference if its diameter is 18 mm?



ID 4502

Geometry and  Measurement K9Estimate the percentage of the circle area compared with the square area.



ID 4561

Geometry and  Measurement K9If I use 30 g of batter to make a crêpe of 30 cm in diameter, how much batter do I need for a 45-cm pancake of the same thickness?

"Archaeological evidence suggests that pancakes are probably the earliest and most widespread cereal food eaten in prehistoric societies." - Wikipedia



ID 4784

Geometry and  Measurement K9How many squares one inch on a side can be fitted into a circle with a three-inch diameter?



ID 4874

Geometry and  Measurement K9What is the surface area of the cube if its side length is 3 cm?



ID 4967

Geometry and  Measurement K9James the Mathematician just measured the angle of his piece of pizza, which is 39.6°.

What part of the pizza did Gerry get?



ID 5125

Geometry and  Measurement K9A solar power station includes 17,000 mirrors, each 60m2.

What is the total area of the mirrors? 

1 km = 1000m


The photograph courtesy of Roland Sauter



ID 5172

Geometry and  Measurement K9Dr Heidi has been called in as an expert to solve a problem. There is a device which is spherical, air-tight when the two halves are glued together, and hollow; it is designed to be thrown into the sea and sit on the sea bed. When she asked them why they said it was hush-hush, top secret, need-to-know, ... and then they looked at her sternly. She hasn’t even seen it for herself. They said its diameter was PI (=3.1415926…) units, but they then said the units were Classified!

They said its weight is exactly 10kg. The sphere has plenty of air space inside.

What should she recommend to make the sphere sit on the sea bed?



ID 5207

Geometry and  Measurement K9Britain’s greatest inventor of mathematical puzzles Henry Ernest Dudeney asked you to place 12 mince pies in 6 lines with an equal number of pies in each line.

What is the largest possible number of pies in a line?