# Tag Archives: area

## 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 Regular Hexagon

What is the ratio of the area of an equilateral triangle to that of a regular hexagon inscribed in the same circle? Source: NCTM Mathematics Teacher, February 2008 Solution The hexagon is made up of six congruent isosceles triangles three … Continue reading

## Area of Trapezoid

In a trapezoid with parallel to , the diagonals intersect at point . The area of triangle is , and the area of triangle is . Find the area of the trapezoid. Source: NCTM Mathematics Teacher, August 2006 Solution Draw … Continue reading

## Round Table

A round table can be made square by dropping the four leaves. If a side of a square table measures inches, to the nearest hundredth of a square inch, how much smaller is the area of the table when 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

## 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

## Length of Side of Square

If the numerical value of the area of a square plus two times the numerical value of its perimeter is equal to , what is the length of one side of the square? Source: NCTM Mathematics Teacher, September 2006 Solution … Continue reading

## Biggest Pizza Slice

An 8-inch pizza is cut into equal slices. A 10-inch pizza is cut into equal slices. A 12-inch pizza is cut into equal slices. A 14-inch pizza is cut into equal slices. From which pizza would you take a slice … Continue reading

## Spring Garden

Each spring, a meter by meter garden has its length increased by meters but its with decreased by centimeters. What will be the maximum attainable area of the garden? Source: NCTM Mathematics Teacher, October 2006 Solution Area in square meters … 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