Find the area of the quadilateral whose side measures 9 cm , 40 cm , 28 cm and 15 cm.The angle between the first two sides of a quad. is a right angle ?

Asked by Vikas | 18th May, 2017, 11:06: PM

Expert Answer:

 
begin mathsize 14px style In space right space triangle space DAB comma
DB squared equals AD squared plus AB squared equals 9 squared plus 40 squared equals 81 plus 1600 equals 1681
rightwards double arrow DB equals square root of 1681 equals 41 space cm
Area space of space triangle DAB equals 1 half cross times AB cross times AD equals 1 half cross times 40 cross times 9 equals 180 space straight m squared
In space triangle DCB comma
2 straight s equals DB plus BC plus CD equals 41 plus 28 plus 15 equals 84 space cm
rightwards double arrow straight s equals 42 space cm
Now comma space area space of space triangle DCB
equals square root of 42 left parenthesis 42 minus 41 right parenthesis left parenthesis 42 minus 28 right parenthesis left parenthesis 42 minus 15 right parenthesis end root
equals square root of 42 cross times 1 cross times 14 cross times 27 end root
equals square root of 15876
equals 126 space straight m squared
Now comma space area space of space quadrilateral space ABCD equals straight A left parenthesis triangle DAB right parenthesis plus straight A left parenthesis triangle DCB right parenthesis equals 180 plus 126 equals 306 space cm squared end style

Answered by Rashmi Khot | 19th May, 2017, 09:39: AM