In the following figure, `/_DAC=30^(@),/_ABC=/_ADC=95^(@)` and `/_BCA=55^(@)`. If the area of `Delta ACD` is `30cm^(2)`, what is the area of `Delta ABC` ?

Explanation

`/_DCA=180^(@)-(95+30)^(@)=55^(@)`
`/_BAC=180^(@)-(95+55)^(@)=30^(@)`
In `Delta ABC` and `Delta ADC`,
`AC=AC` ( common side )
`/_ DAC = /_BAC`
`/_ BCA= /_ DCA`
By ASA congruence property,
`Delta ABC =DeltaADC`
Hence the areas of the triangles are equal.
`implies `Area of `Delta ABC=30 cm^(2)`