Question

Two adjacent sides of a parallelogram are 28cm and 26cm. If one diagonal of it is 30cm long, find the are of the parallelogram

Answer 1

Answer:

672$cm^{2}$

Step-by-step explanation:

draw th fig from the information given in question

given

ab=28cm, ad=26, bd=30 cm

now,semi-perimeter (s) of triangle abd=$\frac{ab+bd+da}{2}$

                                                       =$\frac{30+28+26}{2}$

                                                       =42 cm

accordind to heron's formula area of triangle =$\sqrt{s\times(s-a)\times(s-b)\times(s-c)}$

where s=semi-perimeter of triangle

       a,b,c =sides of triangle

     area of traingle abd=$\sqrt{42\times(42-30)\times(42-28)\times(42-26)}$

=$\sqrt{42\times12\times 14\times16}$

=336$cm^{2}$

hence area of parallelogram abcd =$2\times area of triangle abd$

=$2\times 336$

=672 $cm^{2}$