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Sunday, April 13, 2014

Square, Rectangle, Parallelogram Problems, 7

Category: Plane Geometry

"Published in Vacaville, California, USA"

A garden plot is to contain 200 sq. ft. If its length is to be twice its width, what should its dimension be?

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

The area of a garden lot which is a rectangle is given by the formula


Let x be the width of a rectangle and 2x be the length of a rectangle. If the area of a garden lot is 200 ft² and the length is twice its width, then the above equation becomes








Therefore,



Saturday, April 12, 2014

Circle - Square Problems

Category: Plane Geometry

"Published in Vacaville, California, USA"

Find the area of the largest circle which can be cut from a square of edge 4 in. What is the area of the material wasted?

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

Area of a square:




The edge of a square is equal to the diameter of a circle as shown in the figure above. A circle is tangent to the sides of a square. If the edge of a square is 4 in., then it follows that the diameter of a circle is 4 in. If the diameter of a circle is 4 in., then the radius of a circle is 2 in.

Area of a circle:



or



Therefore, the area of material wasted is




 or



 

Friday, April 11, 2014

Square, Rectangle, Parallelogram Problems, 6

Category: Plane Geometry

"Published in Newark, California, USA"

A window glass is 4 ft. 2 in. by 2 ft. 10 in. Find its area.

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

We notice that the dimensions are not the same because the given units are in feet and inches. Let's convert first all the dimensions in feet only as follows

For the length of a rectangle:
 
 
 
 
 
   
For the width of a rectangle:
 
 
 
 
 
   
Therefore, the area of a rectangle which is a window glass is
 
 
 
 
 
or
   
You can also express your answer in terms of square inches as follows