Square, Rectangle, Parallelogram Problems, 8

Category: Plane Geometry

"Published in Vacaville, California, USA"

The official distance between home plate and second base in a baseball diamond is 120 ft. Find the area of the official ball diamond and the distances between the bases. (The official ball diamond is in the form of a square.)

Solution:

To illustrate the problem, it is better to post and label the picture as follows

Photo by Math Principles in Everyday Life

In this problem, the diagonal of a square is given which is a distance between the home plate and the second base. Since the official ball diamond is a square, then the diagonal bisects the square of side x into two equal isosceles right triangles.

Let x = be the distances between the bases
      d = be the distance between home plate and 2nd base
      A = be the area of official ball diamond 

Apply Pythagorean Theorem in order to solve for the distances between the bases as follows

or

Finally, the area of official ball diamond is

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,

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

 

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