# Tag Archives: area

## 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

## Absolute Value Function

What is the area of the region bounded by the graph of ? Source: NCTM Mathematics Teacher, October 2006 Solution If and If and If and If and The four graphs intersect and form a square of side length . … Continue reading

## Circular Garden

Ebru’s backyard is a square with side length of meters. Her backyard has a circular garden that extends to each side of the yard. In the center of the garden is a square patch of asparagus so big that each … Continue reading

## Area of Triangle

Without using Heron’s formula, find the area of the triangle. Source: NCTM Mathematics Teacher, January 2006 SOLUTION Applying the Law of Cosines Area of triangle Answer: square units Alternative solution 1 Most textbooks state the Law of Sines as We have … Continue reading

## Square in Circle

A square of maximum area is inscribed in a semicircle as shown. What percent of the area of the circle is outside the square? Source: NCTM Mathematics Teacher, January 2006 SOLUTION area of circle = area of square = area … Continue reading

## Circles Within Square

The two circles in the figure are congruent and have their centers on the line . They are tangent to each other and to the square . The radius of the circles is . Calculate the area of the square … Continue reading

## Inscribed Squares

Two squares are inscribed in a semicircle, as shown. The area of the smaller square is . What is the area of the larger square? Source: NCTM Mathematics Teacher, December 2005 SOLUTION is the center of the circle and also … Continue reading