Class 09 To verify that the ratio of the areas of a parallelogram and a triangle on the same base and between the same parallels is 2:1.

 Activity 21

OBJECTIVE                                                                    

To verify that the ratio of the areas of a parallelogram and a triangle on the same base and between the same parallels is 2:1.

METHOD OF CONSTRUCTION

 MATERIAL REQUIRED

Plywood sheet of convenient size, graph paper, colour box, a pair of wooden strips, scissors, cutter, adhesive, geometry box.

 1.   Take a rectangular plywood sheet.

 2.   Paste a graph paper on it.

 3.   Take any pair of wooden strips or wooden scale and fix these two horizontally so that they are parallel.

 4.   Fix any two points A and B on the base strip (say Strip I) and take any two points C and D on the second strip (say Strip II) such that AB = CD.

 Take any point P on the second strip and join it to A and B [see Fig. 1].

DEMONSTRATION

 1.   AB is parallel to CD and P is any point on CD.

 2.   Triangle PAB and parallelogram ABCD are on the same base AB and between the same parallels.

 3.   Count the number of squares contained in each of the above triangle and

 1parallelograms, keeping half square as ₂ and more than half as 1 square, leaving those squares which contain less than half square.

 4. See that area of the triangle PAB is half of the area of parallelograms ABCD.

 OBSERVATION

 1.   The number of squares in triangle PAB =...............

 2.   The number of squares in parallelogram ABCD =............... .

 So, the area of parallelogram ABCD = 2 [Area of triangle PAB] Thus, area of parallelogram ABCD : area of DPAB = ........ : ...........

APPLICATION

 This activity is useful in deriving formula for the area of a triangle and also in solving problems on mensuration.

Note

 You may take different triangles PAB by taking different positions of point P and the two parallel strips as shown in Fig. 2.