Area Of Parallelogram

            Students may not be comfortable in their attempt to develop the area of a parallelogram unless they have a prerequisite knowledge of related terms. It is only good that before embarking on teaching the formula for finding the area of a parallelogram, its definition and other essential definitions be clarified.

            Area is defined as the amount of space occupied or taken up in a plane by a figure. The area is given is square units for instance in², cm², m². Students may want to know what the term ‘plane’ means here. The teacher may define it as a two-dimensional group of points that is made up of infinite lines. He may go ahead and name examples and allow students to name others. The teacher should correct the wrong answers. Parallel lines are two or more coplanar lines that have no points in common or are identical. The teacher should ask students what a Perpendicular lines is. A correct response should be: two segments or lines that form a 90-degree angle. A student can draw this on the board as a demonstration. The teacher then asks what a parallelogram is; it is a quadrilateral with both pairs of opposite lines parallel. A quadrilateral should be explained as a 4-sided shape.

Prior knowledge of area of a triangle, square, rectangle and rhombus will facilitate the development of the formula. Students are likely to ask what a rhombus is and the teacher must explain this and its relationship to a parallelogram: A rhombus is a parallelogram with four equilateral sides. Another term is Angle: it is the union of 2 rays that have the same end point.

 Students may be asked to name various angles. Answers may include a cute, right, obtuse and reflex angles.

             In the attempt to introduce the formula for calculating the area of a parallelogram, the teacher can start by formulating the area of a triangle.

 Material: Use grid paper and pencil

Procedure: Draw a parallelogram and cut it into 2 equal triangles. A parallelogram can be cut out to create 2 equal triangles. And multiplying the area of one of the triangles by 2 can help get the area of a parallelogram. This will enhance the understanding of the concept of a parallelogram and the formula for finding its area.

Materials:

In explaining what a parallelogram is, a manila paper cut-out can be used as a model of a parallelogram. Remember it should be hang at a strategic place in front of the class.

            Models of a square, rectangle and triangle may be helpful. Geoboards can provide a fun way to learn about the concept of area. We can use a 25-pin geoboard. The pins are arranged as shown;

The teacher, together with the learners uses a rubber band to create a number of shapes on the geoboard and they explore the areas using various units of measurements. A rubber band can be used to create a parallelogram in a geo board. This will provide a concrete mode of learning the concept of both the area and the parallelogram.

Note: the learners can use this opportunity to create other shapes.

The students should remember that a parallelogram is a 4-sided shape. Two pairs parallel lines form it. The opposite sides are equal in length and the opposite angles of a parallelogram are equal

            The formula for finding the area of a parallelogram is;

A=b.h

Where by A=area (in square units)

                B=base

                H =height

                 . =Multiply

Remember, the base and height of a parallelogram must be perpendicular. Students should be prompted to remember what perpendicular means. The lateral sides of a parallelogram are not perpendicular to the base therefore a dotted line perpendicular to the base is drawn to represent the height as shown in figure 3 above.

Learners may ask, what is base? It is the length of the parallel lines. (Both have equal length)

Example

Find the area of a parallelogram with a base of 8 inches and a height of 10 inches.

In solving this, the first thing is to remember the formula, which is,

A=b.h

Solution A =(8 x 10) =80in²

            Drawing the parallelogram will enable the learners to have a clearer picture of what they are finding out. Parallelograms can have varied questions. For instance one can be given the area and one of its dimension and asked to find the length of the remaining dimension.

Example

The area of a parallelogram is 24m² if its base is 6 m find the height (Fig4)

Formula A=b.h

                                   h ?

                                                                      Area= 24m²

            24M²=6.H

            24÷6=h

            H=4m

                                       G

                   A               D  E               F

Area (ABCD) =area (BGC) +Area

(AEB)-Area (DEG)

Or area (ABCD)= Area (AFCB)-Area (CDF)

Here, the teaching–learning process must be as interactive as possible. Students may be asked to form groups of 3-5 and look for the various ways they can approach the figure above.

Alternatively the diagram can be drawn on the blackboard. It has to be visible and clearly labeled. Another way of using the above model is to actually fold off the area you are subtracting so that students can see how you arrive at a parallelogram. For instance, in our formula 2 where we stated that area (ABCD) =area (CDF). The teacher and the students can find out area (CDF) to remain with (ABCD). This will be a concrete and manipulative approach and makes learning interesting and interactive.

            In conclusion, the learners should be encouraged to practice a number of challenging exercises. The teacher as a facilitator should help students to master the formula and flexibility.