Math Labs with Activity – Derive a Formula for Finding the Area of a Rhombus (Method 1)

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Math Labs with Activity – Derive a Formula for Finding the Area of a Rhombus (Method 1)

OBJECTIVE

To derive a formula for finding the area of a rhombus by the method of paper folding (Method 1)

Materials Required

  1. A sheet of transparent paper
  2. A geometry box

Theory
It has been geometrically proved that the area of a rhombus is given by area =½ x product of its diagonals.

Procedure
Step 1: Construct any rhombus ABCD on the sheet of transparent paper. Draw its diagonals AC and BD as shown in Figure 28.1. Let and d1 be the lengths of the diagonals AC and BD respectively.
Math Labs with Activity - Derive a Formula for Finding the Area of a Rhombus (Method 1) 1
Step 2: Fold the paper along the diagonals AC as shown in Figure 28.2. What do you observe?
Math Labs with Activity - Derive a Formula for Finding the Area of a Rhombus (Method 1) 2

Observations and Calculations
We observe that when the paper is folded along the diagonal AC, ΔADC exactly covers ΔABC.
Therefore, the triangles ΔABC and ΔADC are congruent.
So, the area of the rhombus is equal to the total area of two congruent triangles (ΔABC and ΔADC).
So, area of tire rhombus ABCD = 2 x area of the ΔABC
=2 x ½ x (d1 x d2/2)   ( see figure 28.2)
= ½ x (d1 x d2)
= ½ x (product of the diagonals).

Result
The area of a rhombus is half the product of its diagonals.

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