The sides of quadrilateral, taken in order are 5, 12, 14 and 15 metres respectively, and the angle contained by the first two sides is a right angle. Find its area.

Explanation

Given that sides of quadrilateral are`AB=5m, BC=12m,CD=14m and DA=15m AB=5m, BC=12m, CD=14 m and DA=15m`
Join `AC In /_\ ABC`(Pythagoras theorem)
Area of quadrilateral `ABCD=area of (/_\ABC) + Area of (/_\ADC)`
Area of `/_\ ABC,is=1/2xxABxxAC`
`=>1/2xx5xx12=30 cm^2`
In`(/_\ABC),AC^2=AB^2+BC^2`
`AC^2=5^2+12^2=169`
`AC=sqrt169=13`
Now in triangle ADC,2S be the perimeter.
`2s=AD+DC+AC=15+14+13`
`S=1/2(42)=21m`
Area of `/_\ADC=sqrt(S(S-AD)(S-DC)(S-AC)`
`=>sqrt(21(21-15)(21-14)(21-13)`
`=>sqrt(21xx6xx7xx8)=84cm^2`
Area of quadrilateral`ABCD=30+84=114cm^2`