1.

A park, in the shape of a quadrilateral ABCD, has `/_C=90^o , A B=9 m , B C=12 m , C D=5 m a n d A D=8 m`. How much area does it occupy?

Answer» We can create a diagram with the given details.
Please refer to video for the diagram.
Now, `ar(BCD) = 1/2**12**5 = 30m^2`
Also, `BD = sqrt(12^2+5^2) = sqrt169 = 13m`So, in `Delta ABD`
`a = 8m,b=9m,c=13m`
So, `s = (a+b+c)/2 = (8+9+13)/2 = 15m`
So, `ar(ABD) = sqrt(s(s-a)(s-b)(s-c))`
`ar(ABD)=sqrt(15(15-8)(15-9)(15-13)) = sqrt(15**7**6**2)=6sqrt35m^2`
So, `ar(ABCD) = ar(BCD)+ar(ABD) = 30+6sqrt35m^2`


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