question_answer

ABCD is a quadrilateral in which diagonal BD = 64cm. AL \[\bot \] BD and CM \[\bot \] BD, such that AL = 13.2 cm and CM = 16.8 cm. The area of the quadrilateral ABCD in square centimetres is

A)  422.4                          

B)  690.0

C)  537.6                          

D)  960.0

Correct Answer: D

Solution :

      Area of quadrilateral ABCD = Area of \[\Delta \]ABD + Area of \[\Delta \]BCD \[=\frac{1}{2}\times BD\times AL+\frac{1}{2}\times BD\times CM\] \[=\frac{1}{2}\times BD(AL+CM)\] \[=\frac{1}{2}\times 64(13.2+16.8)\] \[=\frac{1}{2}\times 64\times 30=960\] sq. cm