Tag Archives: geometry

Making Triangles

You have six sticks of lengths , and cm. Find the number of noncongruent triangles that can be formed using three of these sticks as sides. Source: NCTM Mathematics Teacher, August 2006 Solution Three sticks make a triangle. There are … Continue reading

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Two Equilateral Triangles

If two equilateral triangles of area intersect to form a regular hexagon, then what is the area of the hexagon? Source: NCTM Mathematics Teacher, September 2006 Solution If we subdivide an equilateral triangle into smaller congruent equilateral triangles as shown … Continue reading

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Two Squares

If the vertices of square are the midpoints of the edges of square , then what is the ratio of the area of square to square ? Source: NCTM Mathematics Teacher, September 2006 Solution The diagonal of square divides square … Continue reading

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Maximum Angle

The measures of five angles of a convex polygon are each equal to . In which of the five open intervals does the maximum angle of all such polygon lie? (a) (b) (c) (d) (e) Source: NCTM Mathematics Teacher, September … Continue reading

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Length of Hypotenuse

Consider the line containing the points and . What is the length of the hypotenuse of the right triangle formed by the intersections of and the -and -axes? Source: NCTM Mathematics Teacher, September 2006 Solution Points , and are the … Continue reading

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Rolling Wheel

If a wheel completes exactly revolutions while rolling feet, what is the diameter of the wheel? Source: NCTN Mathematics Teacher, September 2006 Solution The above figure shows the ground distance traveled by the rolling wheel of radius feet in revolutions. … Continue reading

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Ball and Cube

Suppose that the volume of a ball is equal to times the volume of a cube. What is the ratio of the surface area of the ball to that of the cube? Source: NCTM Mathematics Teacher, September 2006 Solution Let … Continue reading

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Which Triangle is Largest?

Of the following triangles given by the lengths of their sides, which one has the greatest area? (a) (b) (c) (d) (e) Source: NCTM Mathematics Teacher, September 2006 Solution Heron’s Area Formula: area = where and are the lengths of … Continue reading

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Area of a Disc

If the area of a disc inscribed in a square is square centimeters, what is the area of the square? Source: NCTM Mathematics Teacher, September 2006 Solution Area of disc = Area of square = Answer: square centimeters

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Arc of a Circle

is a diameter of a circle of radius unit. is a chord perpendicular to that cuts at . If the arc is of the circumference of the circle, what is the length of the segment ? Source: NCTM Mathematics Teacher, … Continue reading

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