ID 593

Geometry and  Measurement K8A square has an area of 30 m2. What is the length of its side?



ID 594

Geometry and  Measurement K8John walks for one and a half hours at an average speed of 5.5 km/h.
Then he walks for one and a half hours at an average speed of 5 km/h.
Then he walks for one and a half hours at an average speed of 4.5 km/h.

How far does John walk?



ID 601

Geometry and  Measurement K8Identify the shape with the largest perimeter.



ID 602

Geometry and  Measurement K8Identify the ratio

AB:BD.



ID 603

Geometry and  Measurement K8What is the length of BC in the right-angled triangle?



ID 607

Geometry and  Measurement K8Which pair of angles in this figure has the same measurement?



ID 608

Geometry and  Measurement K8There are 2 parallel lines in the figure.

What is the measure of angle x?



ID 609

Geometry and  Measurement K8What is the greatest number of cubes with a side length of 3 centimeters that can fit in this box?



ID 611

Geometry and  Measurement K8If each edge length of this shape is doubled, what will happen to its volume?



ID 612

Geometry and  Measurement K8A curtain covers a window as shown on the right.
We approximate the area of the curtain by 2 triangles.
The area of the window is 2 square meters.
How much of the window area is covered by the curtain?



ID 616

Geometry and  Measurement K8Which one of the triangles is not always similar to the others?



ID 618

Geometry and  Measurement K8Which angle is largest?



ID 619

Geometry and  Measurement K8Which angle is smallest?



ID 623

Geometry and  Measurement K8Find the value of X.



ID 624

Geometry and  Measurement K8Archery target faces have five colors, with each color divided into two parts to provide scoring zones.

The figure shows ten concentric circles. The rings have the same width as the radius of the innermost circle.

What is the difference between the white and yellow areas?



ID 626

Geometry and  Measurement K8Find the mirror line.



ID 627

Geometry and  Measurement K8Find the center of rotation.



ID 629

Geometry and  Measurement K8What is the size of angle X?



ID 634

Geometry and  Measurement K8Which segment length is the smallest?



ID 636

Geometry and  Measurement K8How many right angles are possible in a polygon with five sides?



ID 637

Geometry and  Measurement K8Which drawing represents the top view of this figure?



ID 638

Geometry and  Measurement K8Which triangle has angles that appear to measure 40°, 60° and 80°?



ID 639

Geometry and  Measurement K8Which figure can be rotated 60° about its center and have its final orientation appear the same as the original orientation?



ID 640

Geometry and  Measurement K8Find the shape

that has fewer than 15 sides and
at least one 90° angle.



ID 641

Geometry and  Measurement K8In the diagram, the radii of the two concentric circles are 5 and 10, respectively.
What fraction of the bigger circle is shaded?



ID 642

Geometry and  Measurement K8If two sides of the triangle have lengths of 11 and 22, which of the following could be the perimeter of the triangle?



ID 643

Geometry and  Measurement K8Which shape has the largest shaded region in terms of area?



ID 645

Geometry and  Measurement K8In the diagram, triangle ABC is an isosceles.

How many different angles are there?



ID 646

Geometry and  Measurement K8A 7x7x7cube is painted, and then cut into 1x1x1 cubes.

How many of the cubes are not painted?



ID 648

Geometry and  Measurement K8Ten cubes are glued together, and then the entire figure is painted.

How many cube faces are covered in paint?



ID 650

Geometry and  Measurement K8The green area 'G' is 80% of the entire area of the rectangle.

Find x.



ID 652

Geometry and  Measurement K8If 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 654

Geometry and  Measurement K8The figure shows a regular hexagon.

What is the fraction of the area of the colored part to the area of the entire shape?



ID 655

Geometry and  Measurement K8Which of the following cubes can be folded from this net?



ID 659

Geometry and  Measurement K8I strike a pool ball from corner A of the rectangular billiard table at an angle of 45°.

In which corner pocket will the ball fall into?



ID 673

Geometry and  Measurement K8A cross-shaped lawn has a 1-meter wide path that surrounds it.
Each side of the lawn is 5 meters in length.

What is the area of the path?



ID 674

Geometry and  Measurement K8The height of a cylinder is decreased by 10%, and the radius of the cylinder is increased by 10%.
Estimate and compare the volume of the new cylinder to the first one.



ID 1206

Geometry and  Measurement K8What is the area of a square with a diagonal of length 8?



ID 1335

Geometry and  Measurement K8Estimate the difference between the smallest and largest areas of the columns.



ID 1407

Geometry and  Measurement K8A net can be folded into a cube.

Which of the faces is opposite the face marked red?



ID 1445

Geometry and  Measurement K8Find the missing part.

Remember, there may be more than one correct answer.



ID 1464

Geometry and  Measurement K8Which of these diagrams could be drawn without taking the pen off the page and without drawing along a line twice?



ID 1471

Geometry and  Measurement K8I place a digital clock on a mirror.
The time 18:30 on the clock reads the same when it is reflected in the mirror.

What other time has the same property?



ID 1472

Geometry and  Measurement K8Small blue squares have the same size.

What share of the large square is blue?



ID 1489

Geometry and  Measurement K8Find the area of the triangle.



ID 1520

Geometry and  Measurement K8This shape was formed by removing a small cube from a big cube.
The volume of the removed cube is 1/4 of the big cube's volume.

Find the surface area of the shape compared with the surface area of the big cube.



ID 1528

Geometry and  Measurement K8How many green triangles are needed to completely cover the square?



ID 1568

Geometry and  Measurement K8How many blue T-shapes can be placed inside the 5x5 square without intersecting each other?

Find the greatest number.



ID 1656

Geometry and  Measurement K8The game Battleship (Battleships or Sea Battle) is a guessing game played by two people.

How many four-space battleships can you place on the 10 x 10 grid ?

Each battleship must be either vertical or horizontal, in other words not at any sort of angle.
The battleships must not touch each other, even at their corners.



ID 1687

Geometry and  Measurement K8How many pairs of beads are at a distance apart which is smaller than the length of the line segment AB?

The distance between the beads is the distance between beads' centers.



ID 1693

Geometry and  Measurement K8Estimate how many times larger the perimeter of the red triangle is compared with the perimeter of the blue triangle.

Both triangles are equilateral.



ID 1713

Geometry and  Measurement K8The picture shows a regular polygon.

Which two lines are parallel?



ID 1765

Geometry and  Measurement K8How many points exist where the rays intersect?



ID 1770

Geometry and  Measurement K8ABCD is a rectangle.
E, F, G and H are midpoints of AO, BO, CO and DO respectively.

What is the fraction of EFGH to ABCD?

Compare the perimeters.



ID 1824

Geometry and  Measurement K8I am using red and yellow tiles to make the pattern shown on the right.

There are 6 tiles in the second 'circle'.

If I continue the pattern in the same way, how many tiles will be in the 100th "circle"?



ID 1836

Geometry and  Measurement K8A honey bee is walking from point A to point B along the indicated path.

If the cells are regular hexagons with 4 mm long sides, what is the length of the path AB?



ID 1840

Geometry and  Measurement K8What fraction of the square is red?



ID 1845

Geometry and  Measurement K8Alex is framing a small flower box by four rectangular bricks.
Each of the rectangles has a perimeter of 80 cm.

What is the perimeter of the entire box?



ID 1846

Geometry and  Measurement K8An ant goes from A to B along the indicated path in the equilateral triangle with sides that have a length of 5.
The distance between the horizontal lines is the same as the distance between point A and the first line.
The horizontal pathways are parallel to BC.

How long is the entire path?



ID 1857

Geometry and  Measurement K8If the red area is five times smaller than the blue area, what is X?



ID 1871

Geometry and  Measurement K8What is the ratio of the shaded area to the area of the big circle?



ID 1906

Geometry and  Measurement K8What is the measure of the marked angle in the regular hexagon?



ID 1982

Geometry and  Measurement K8What is the angle between the hour hand and the minute hand at 14:20?



ID 2082

Geometry and  Measurement K8Guesstimation.

How many the small triangles would be needed to cover the trapezoid?



ID 2152

Geometry and  Measurement K8In a city Konigsberg, there were seven bridges.
There was a tradition to walk and cross over each of the seven bridges.
If a young man starts and finishes at the same point, what is the smallest number of crossings he would have to make?



ID 2236

Geometry and  Measurement K8The circles are equally spaced.

Find 2 regions of equal area. One of them is a circle.
Which one?



ID 2300

Geometry and  Measurement K8Find perimeter of a square that consists of two rectangles with perimeters 20 and 16 units.



ID 2301

Geometry and  Measurement K8How many apples at equal distances from each other can I have?



ID 2939

Geometry and  Measurement K8The shape is turned 315o clockwise.

Find the new position of point A.



ID 2940

Geometry and  Measurement K8The volume of a box is 3000 cm3.
The ratio of the box length, width and height is

4:3:2 (length : width : height, respectively)

What could its length be?



ID 2944

Geometry and  Measurement K8What is the area of the shape with 4 axes of symmetry?



ID 2947

Geometry and  Measurement K8The shape is to be reflected 4 times over the vertical line y and then reflected over the horizontal line x. Find its new position.



ID 2949

Geometry and  Measurement K8Find the largest side.



ID 2966

Geometry and  Measurement K8Two boys, starting at the same point,
walk in opposite directions for X meters,
turn right and walk another Y meters,
turn right and walk another X meters and then
turn right and work another Y meters.

What is the distance between them?



ID 2971

Geometry and  Measurement K8A 7x7x7cube is painted, and then cut into 1x1x1 cubes.

How many of these cubes are painted?



ID 2981

Geometry and  Measurement K8The shape is composed of squares and isosceles triangles.

What percentage of the shape is white?



ID 2983

Geometry and  Measurement K8Four people start from the same point.
A walks northwest at 1 km/h.
B walks north at 4 km/h.
C walks east at 3 km/h.
D walks south at 1 km/h

Which people have the greatest distance between them after a one hour walk?



ID 3001

Geometry and  Measurement K8John walks for one and a half hours at an average speed of 5 mph.
Then he walks for one and a half hours at an average speed of 4 mph.
Then he walks for one and a half hours at an average speed of 3 mph.

How far does John walk?



ID 3012

Geometry and  Measurement K8There are 2 parallel lines in the figure.

What is the measure of angle x?



ID 3013

Geometry and  Measurement K8What is the greatest number of cubes with a side length of 1.49 cm that can fit in this box?



ID 3029

Geometry and  Measurement K8Which two segments have the same length?



ID 3068

Geometry and  Measurement K8A hall is cube-shaped.
The volume of the hall is 343 cubic meters.

Find the length of a side of the floor.



ID 3072

Geometry and  Measurement K8What is the longest path?



ID 3073

Geometry and  Measurement K8One 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 length of the box?



ID 3074

Geometry and  Measurement K8One 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 width of the box?



ID 3202

Geometry and  Measurement K8For what X is the area of triangle ADE four times larger than the area of triangle ABC?



ID 3229

Geometry and  Measurement K8Which is the closest to the value of the midpoint between 282 millimeters and 30 centimeters?



ID 3314

Geometry and  Measurement K8A school garden is 4 units long and 3 units wide.

How many bushes a unit apart can be placed along the edges?



ID 3402

Geometry and  Measurement K8Which shape has the smallest area?



ID 3533

Geometry and  Measurement K8Which set of circles has the largest perimeter?



ID 3534

Geometry and  Measurement K8Which set of circles has the largest area?



ID 3550

Geometry and  Measurement K8How many cubes can be deleted from the tower so that the top cube does not move?



ID 3574

Geometry and  Measurement K8What is the largest hollow cube that I can construct from 500 small cubes?



ID 3631

Geometry and  Measurement K8Two towers have the same height.

Find the ratio of the width to the height of the bricks.



ID 3641

Geometry and  Measurement K8If the area of the square is B and the area of the circle is C, what is the area of the shape enclosed by the thick black line?



ID 3642

Geometry and  Measurement K8All three bridges have the same horizontal width a.

Which bridge has the largest area?



ID 3653

Geometry and  Measurement K8The figure shows a vertical cross-section of a road.

Which part of the road is heavier?



ID 3667

Geometry and  Measurement K8Find the area of the red shape if the area of a small triangle is 1 square unit.



ID 3676

Geometry and  Measurement K8The 5 x 5 grid contains squares of different sizes from 1 x 1 to 5 x 5.
How many squares don't contain the red square?



ID 3773

Geometry and  Measurement K8Compare the areas of the squares B and A.



ID 3789

Geometry and  Measurement K8A set of 119 one-unit wooden cubes is packed on one level in a rectangular tray.
What is the minimum perimeter that the tray can have?



ID 3796

Geometry and  Measurement K8What is the difference between the red area and the blue area if the numbers show the areas of each square?



ID 3798

Geometry and  Measurement K8What fraction of the large square is shaded?



ID 3800

Geometry and  Measurement K8The border of this shape is composed of four semi-circles, each with a radius of 2 units.

What is the area of the shape?



ID 3968

Geometry and  Measurement K8What is the maximum area of a triangle inside a unit square?



ID 3995

Geometry and  Measurement K8How many 4 cm by 4 cm squares can I obtain from a wire that is 100 cm long?



ID 4034

Geometry and  Measurement K8How many signs have a line of symmetry?



ID 4108

Geometry and  Measurement K8Find the number.



ID 4352

Geometry and  Measurement K8I want to cut the cross by two straight cuts to make the greatest number of pieces.

What is the largest number of pieces I can get?



ID 4415

Geometry and  Measurement K8What is the maximum number of points of intersection of five distinct straight lines in a plane?

This is a typical SAT question.



ID 4549

Geometry and  Measurement K8Find the external surface area of the pyramid if each cube side is 1 unit.

Don't count the bottom and the internal surfaces.



ID 4812

Geometry and  Measurement K8An arrangement is formed by laying nine colored squares of the same size one over another.

Which square is laid at the bottom?



ID 4843

Geometry and  Measurement K8I divided a 3 x 4 square into 6 squares.

What is the smallest number of squares into which you can divide a 6 x 7 rectangle?

Author: Matt Enlow



ID 4846

Geometry and  Measurement K8What is the smallest area of a rectangle which includes all five squares?



ID 4854

Geometry and  Measurement K8If the height of the tower is 88 mm, estimate the height of a tower that uses 100 pens.



ID 5058

Geometry and  Measurement K8The sum of the perimeters of three rectangles of the same area is 172cm.

What is the largest possible sum of their areas?



ID 5102

Geometry and  Measurement K8Divide the square into four equal shapes, so that each shape includes a circle.

How many sides does the shape have?



ID 5106

Geometry and  Measurement K8I spent 10 minutes to paint the upper part of the shape in blue.

How much time do I need to paint the remaining part?



ID 5153

Geometry and  Measurement K8I cut two or three corners off an equilateral triangle, each cut being straight.

What resulting shape is possible?



ID 5285

Geometry and  Measurement K8The picture shows a collection of squares. If the smallest squares have a side length of 1m, what is the area of entire figure?



ID 5295

Geometry and  Measurement K8Find the area of the blue arrow.