# Tag Archives: rectangle

## Four Congruent Rectangles

Four congruent rectangles are arranged as shown in the figure to form a large rectangle. The area of the large rectangle is . What is the area of a square that has the same perimeter as the large rectangle? Source: … Continue reading

## Equilateral Triangle and Square

A pentagon made up of equilateral triangle with side length on top of square is inside a circle passing through points , and . Find the radius of the circle. Source: NCTM Mathematics Teacher, August 2006 Solution Let be the … Continue reading

## 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

## Rectangle Inside a Square

An isosceles right triangle is removed from each corner of a square piece of paper so that a rectangle remains. What is the length of a diagonal of the rectangle if the sum of the areas of the removed pieces … Continue reading

## Four Squares

A rectangle with side lengths and is divided into squares as shown. What is the value of ? Source: NCTM Mathematics Teacher, December 2005 SOLUTION Sum of the areas of the squares equals the area of the rectangle (extraneous solution) … Continue reading

## Parallelogram

is a parallelogram with , and . If the area of the parallelogram is , what is the value of ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION Draw a perpendicular to . If the x-coordinate of equals , its … Continue reading

## Measure of Angle

Let be a rectangle with , and let be an equilateral triangle. and intersecting (not the extension of ) at and , respectively. If is the midpoint of , how many degrees are in angle ? Source: NCTM Mathematics Teacher … Continue reading

## Midpoints of Four Sides

The midpoints of four sides of a regular hexagon can be connected to create a trapezoid, a kite, or a rectangle. Which two quadrilaterals formed in this manner have equal areas, and what fraction of the hexagon’s area do they … Continue reading

## Area of Rectangle

A triangle has side lengths , and . The area of the rectangle with side lengths and is a two-digit number, with both digits equal to . The sum of the digits in is one-third the value of . What … Continue reading