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Question

Find the area of a rhombus one side of which measures 20 cm and one of whose diagonals is 24 cm.


Solution

Let ABCD is a rhombus with the diagonals AC and BD which intersect each other at O.

Given AC = 24cm.

Then AO = 12cm.

Let BO = x and AB = 20cm.

By Pythagoras theorem, we know that 

c2=a2+b2

202=122+x2

400=144+x2

x2=400144

x2=256

x = 16cm.

Diagonal BD = 2 * 16

                      = 32cm.

We know that Area of the rhombus = 1/2 * (product of diagonals)

                                                            = 1/2 * 24 * 32

                                                            = 12 * 32

                                                            = 384 sq.cm.



 


Mathematics
Secondary School Mathematics IX
Standard IX

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