ID 853

Geometry and  Measurement K11A rectangle has a width of 0.3x and a length of 0.4x.

Which formula is the correct one to calculate the perimeter (P) in terms of x?



ID 854

Geometry and  Measurement K11Which gives the largest answer?



ID 858

Geometry and  Measurement K11The edges of a large cube are 3 times longer than the edges of a small cube.

How many times greater is the volume of the large cube than the small cube?



ID 863

Geometry and  Measurement K11An arrow rotates 366° in one second.

How many revolutions does it make in one minute?



ID 868

Geometry and  Measurement K11Two satellites orbit at 1/4 R above Earth's surface. R is the radius of the Earth.

What is the maximum distance at which the two satellites can see each other?



ID 869

Geometry and  Measurement K11A mathematician wants to approximate the width of a lake.
He places 5 markers near the lake and measures the distances shown in the diagram.

What is the width of the lake in meters (m) from point P to point Q?



ID 870

Geometry and  Measurement K11What transformation creates an image with a vertex at the origin?



ID 872

Geometry and  Measurement K11What is the area of the colored shape?



ID 873

Geometry and  Measurement K11Angles A and C are equal to 90o.

Which proportion is true?



ID 874

Geometry and  Measurement K11 Each interior angle of a regular polygon measures 144o.

How many sides does the polygon have?



ID 878

Geometry and  Measurement K11A square garden is 401 square meters.
The minimum distance between apple trees is 5 meters. The minimum distance between a tree and the fence around the garden is 5 meters.

How many trees are there?



ID 879

Geometry and  Measurement K11If the Earth's radius is twice the radius of planet M, then how much bigger is the Earth's volume?



ID 882

Geometry and  Measurement K11A boy is making boxes from cardboard.
He is going to cut square pieces off each corner as shown in the diagram and fold the sides up.
Which size of square pieces would give a larger box in terms of volume?



ID 884

Geometry and  Measurement K11Alex wants to arrange the cylinders from least to greatest volume.

What is the correct order?



ID 889

Geometry and  Measurement K11Which shape would be made if the two sections were fitted together?



ID 896

Geometry and  Measurement K11Five boys Andrew, Brandon, Chris, Daniel, and Ethan live on State Street.

At which point should the children meet so that the sum of the distances they walk to that point is minimized?



ID 897

Geometry and  Measurement K11A boy cuts a cardboard circle and only cuts 5 straight lines.
He does not care if the pieces are equal.

What is the maximum number of pieces he can obtain if he makes 5 cuts without moving the cut pieces?



ID 898

Geometry and  Measurement K11How many planes of symmetry does a cube have?



ID 904

Geometry and  Measurement K11How many boxes measuring 0.1m x 0.1m x 6.9m can be packed into a container measuring 6m x 3m x 2m?



ID 905

Geometry and  Measurement K11The figure shows a pyramid made of small squares.
I want to move the small squares and transform the pyramid into a big square.

What is the lowest possible number of moves that need to be made?



ID 915

Geometry and  Measurement K11The American flag consists of thirteen equally spaced, horizontal red and white stripes, with a blue rectangle in the canton bearing fifty small, white, five-pointed stars.

What part of the flag is red?



ID 919

Geometry and  Measurement K11The figure shows a regular pentagon.


Compare the values of angles A and B.



ID 988

Geometry and  Measurement K11Divide the analog watch face with two straight lines so that the sums of the numbers in each part are equal.

Which is true?



ID 1013

Geometry and  Measurement K11Look at the mini-golf course.

To what point would the player hit the golf ball to make a hole-in-one?



ID 1032

Geometry and  Measurement K11How many interior right angles are possible in a polygon with seven sides?



ID 1042

Geometry and  Measurement K11Bill mows the front lawn, which is a 7m by 10m rectangle.
The mower cuts a 1m wide strip.

If Bill starts at the corner and mows around the lawn in a spiral toward the center, how many times around must he go before he has mowed the lawn?



ID 1075

Geometry and  Measurement K11Among the following shapes of equal area, which has the largest perimeter?



ID 1223

Geometry and  Measurement K11A block of wood in the form of a cuboid 9 x 10 x 11 has all its six faces painted red.

If the wooden block is cut into small cubes of 1 x 1 x 1, how many of these cubes would have red paint on them?



ID 1250

Geometry and  Measurement K11I fold a square piece of paper in half four times without unfolding, making an isosceles right triangle each time.

What is the correct net of the creases on the paper after unfolding the paper?



ID 1252

Geometry and  Measurement K11How many squares can be formed by joining four of these points on the rectangular grid?



ID 1253

Geometry and  Measurement K11If I tile a floor with 3000 regular hexagonal tiles as shown here how many green tiles do I need?



ID 1259

Geometry and  Measurement K11Path C consists of straight segments.
Path D and E consist of semi-circles.

Which path is the longest?



ID 1279

Geometry and  Measurement K11 A circle is drawn through two vertices of a square so that it is tangent to one side of the square.
The square has sides of length 8.

Find the radius of the circle.



ID 1352

Geometry and  Measurement K11I placed together four identical triangles and the square, without overlaps, to form a figure.

What is the least possible perimeter of the new figure?



ID 1353

Geometry and  Measurement K11Compare areas F and G



ID 1398

Geometry and  Measurement K11What is the sum of the marked angles?



ID 1401

Geometry and  Measurement K11Eight points are equally spaced on a circle.

How many right angled triangles that have all their vertices at three of these points can you draw?



ID 1444

Geometry and  Measurement K11The picture shows six equilateral triangles.
The sides of the triangles are three times longer than are the side of the regular hexagon.

What fraction of the whole shape is blue?



ID 1462

Geometry and  Measurement K11The picture shows a tiling pattern which is made of square green tiles 10 x 10 cm and gray tiles 20 x 10 cm.
The pattern is extended to cover a large surface.

What fraction of the surface is colored green?



ID 1483

Geometry and  Measurement K11Fifteen 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 decreased by 20%?



ID 1487

Geometry and  Measurement K11What is the smallest number of segments that needs to be moved so that the pattern has a line of symmetry?



ID 1526

Geometry and  Measurement K11All three circles are tangent to the horizontal line and to one another.
The diameter of the small circle is 2.

Find the diameter of the big circles.



ID 1578

Geometry and  Measurement K11A girl wants to cut the paper into several equal pieces of the same shape, and with nothing left over.

(NOTE: She does not have to cut along the dotted lines.)

How many pieces are possible?



ID 1755

Geometry and  Measurement K11Two lines and two diagonals are drawn through the center of the rectangle.
What fraction of the area of the rectangle is green?



ID 1807

Geometry and  Measurement K11How many circles are needed to separate each star from all of the others?



ID 1811

Geometry and  Measurement K11I would like to cut the shape into the fewest possible pieces that will fit together and form a rectangle.

What is the smallest number of pieces?



ID 1848

Geometry and  Measurement K11The colored figure at the picture consists of isosceles right triangles.

What is the largest possible area of the blue shape?



ID 1865

Geometry and  Measurement K11The vertices of the smaller square divide each side of the larger square by a ratio of 2:1.

What fraction of the larger square is blue?



ID 1966

Geometry and  Measurement K11I blew some air into a spherical balloon and quadrupled its surface area (4 times).

By how much did I multiply the volume of the sphere?



ID 1977

Geometry and  Measurement K11Estimate the area of the largest equilateral triangle that can fit within a 1x1 square.



ID 2158

Geometry and  Measurement K11Four matchsticks form a square.

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

Note: The matchsticks do not intersect each other.



ID 2186

Geometry and  Measurement K11Guesstimation.

How many tennis balls can fit in a school bus?



ID 2188

Geometry and  Measurement K11What is the maximum number of apples (ideal spherical units) that can touch another given apple (spherical unit) without overlapping?



ID 2200

Geometry and  Measurement K11I arranged twelve one-inch wooden sticks in a polygon with an area of 6 square inches.
I would like to form a polygon with an area of 4 square inches using these 12 sticks.

What is the minimum number of sides of the new polygon?



ID 3113

Geometry and  Measurement K11Which reservoir has the smallest volume?



ID 3114

Geometry and  Measurement K11Anna has made puzzle pieces by cutting wedges from a disk.
Each wedge cut from the disk has a 50-degree angle at the center of the disk.
The weight of the uncut disk is 108 grams.

How many grams does each 50-degree wedge weigh?



ID 3115

Geometry and  Measurement K11How many coins do I need to melt down and recast to get a single coin of double thickness and double diameter?



ID 3123

Geometry and  Measurement K11Shape A and B are congruent equilateral triangles.
Shape C is formed by superimposing shapes A and B by about their centers.

What is the perimeter of shape C if the perimeter of shape A is 45 inches?



ID 3124

Geometry and  Measurement K11The diagram illustrates a row of three squares formed by matches.

How many matches will it take to make a row of 33 squares?



ID 3162

Geometry and  Measurement K11A boy stacked colored cubes in a square pyramid like the one shown here.
The top layer had 1 cube, the second layer had 4 cubes, and so on.

If the pyramid were 16 layers high, how many cubes would be in the sixteenth layer?



ID 3163

Geometry and  Measurement K11The figure shows a red equilateral triangle inscribed within another equilateral triangle. The side of the bigger triangle measures 10 meters.

What is the ratio of blue area to the total area of the largest triangle?



ID 3168

Geometry and  Measurement K11The three circles have fixed centers, and the diameter of a circle is 7 / 8 of its 'left neighbor'.

The left circle completes a hundred revolutions per minute.

Estimate how many revolutions the right circle completes.



ID 3173

Geometry and  Measurement K11For this rectangular solid, which plane(s) contain(s) C and is/are parallel to plane AEF?



ID 3174

Geometry and  Measurement K11Two similar pyramids have volumes of 343 m3 and 64 m3.

What is the ratio of their surface areas?



ID 3224

Geometry and  Measurement K11Among the following shapes of equal perimeter, which has the smallest area?



ID 3651

Geometry and  Measurement K11Which triangle with sides a, b, and c has the largest area?



ID 3762

Geometry and  Measurement K11Squares 1, 2 and 3 have sides of length 1, 2 and 3 units, respectively.

What is the perimeter of the entire figure if there are 100 such squares in the shape?



ID 3791

Geometry and  Measurement K11A square with a side length 20 has two vertices on the circle, and one side touching the circle.

Find the diameter of the circle.



ID 3928

Geometry and  Measurement K11Two squares, each with sides measuring 2 cm, are placed such that a vertex of one lies at the center of the other.

What is the area of the overlapping region?



ID 3934

Geometry and  Measurement K11A recipe makes 5 pizzas that are 12 inches in diameter.

If I decide to make 3-inch diameter pizzas, how many of the smaller pizzas would this recipe make?



ID 3935

Geometry and  Measurement K11Two congruent circles share a radius.

What is the perimeter of the figure compared with the perimeter of the original circle?



ID 3951

Geometry and  Measurement K11What is the area of a garden?



ID 3966

Geometry and  Measurement K11The large and small circles touch each other.

What part of the large circle is shaded?



ID 4013

Geometry and  Measurement K11Estimate how long the rope is if its diameter is 1 cm.



ID 4049

Geometry and  Measurement K11Find the ratio of the areas of the large and small squares.



ID 4075

Geometry and  Measurement K11What is the largest possible side size of an equilateral triangle that fits into a square with a side size 10?



ID 4166

Geometry and  Measurement K11The hypotenuse of a right triangle is 6, and the length of one leg is 2 units longer than the length of the other.

What’s the area of the triangle?



ID 4231

Geometry and  Measurement K11What part of the rectangle is red if points A and B are the midpoints of the corresponding sides of the rectangle?



ID 4325

Geometry and  Measurement K11How many lines can be drawn in a plane so that they are equidistant from 3 points?



ID 4427

Geometry and  Measurement K11 Three overlapping squares form 5 squares including themselves in the picture.

What is the greatest number of squares you can make by overlapping three squares of the same size?



ID 4430

Geometry and  Measurement K11You have a 5kg weight and a 12kg weight.
They are the same height and are made from the same material.

What is the ratio of their diameters?



ID 4714

Geometry and  Measurement K11Estimate the maximum number of smaller 1-inch circles that fit in a larger circle, the diameter of which is 2.9 times larger.



ID 4863

Geometry and  Measurement K11What is the volume in cubic inches of the pyramid with height 10 inches?

The pyramid consists of equal cubes.



ID 5039

Geometry and  Measurement K11I want to divide this shape into four congruent pieces - all of precisely the same size and shape.

How many sides do the four pieces have?



ID 5051

Geometry and  Measurement K11Which pyramid has the largest volume?



ID 5115

Geometry and  Measurement K11Find the area of the colored rectangle.



ID 5160

Geometry and  Measurement K11Which line goes through the center of the circle?



ID 5304

Geometry and  Measurement K11All sides of the white cross is the same.

What percentage of the square is the cross?