# Problem Solving Involving Quadrilaterals

By | August 15, 2010

‘To understand mathematics is to make connections.’ This is one of the central ideas in current reforms in mathematics teaching. Every question, every task a teacher prepares in his/her math classes should contribute towards strengthening the connections among concepts. There are many ways of doing this. In this post I will share one of the ways this can be done: Use the same context for different problems.

The following are some of the problems that can be formulated based on quadrilateral BADF.  You can pose these problems to your class but the best way is to simply show the diagram to the students then ask them to formulate the problems themselves.

###### Problem #1. What is the area of the quadrilateral? Show different methods.

The solution to this question depends on the grade level of students. The one shown below can be done by a Grade 5 or 6 student.

Area of a quadrilateral

###### Problem #2. What is the perimeter of the quadrilateral?

One solution is to construct squares around the quadrilateral. The length of the sides of the quadrilateral is the square root of the area of the squares. The areas of the square are 8, 10, 5 and 17  sq units. Hence the perimeter is $\sqrt8+\sqrt{10}+\sqrt5+\sqrt{17}$ units. Of course the Pythagorean Theorem will also be a handy tool.

Finding the perimeter of a quadrilateral

###### Problem #3. Construct quadrilaterals equal in area to BADF.

The following figure gives the hint on how to do this.

Constructing quadrilaterals with the same area

Click here or the figure below for another hint in GeoGebra applet.

Constructing quadrilaterals with equal area

###### Problem #4. Construct a pentagon equal in area to BADF.

This shouldn’t be a problem after solving #3.

## 5 thoughts on “Problem Solving Involving Quadrilaterals”

1. Mr Writer

Great post! I haven’t seen the method of segmenting the shape into rectangles and triangles before. This is a really good method that most kids would definitely understand. Thank you!