Question

ABCD is a parallelogram and X is the mid-point of AB. `(AXCD)= 24 cm^(2)`, then `ar (ABC) = 24 cm^(2)`.

Answer 1

False
Given, ABCD is a parallelogram and `ar (AXCD) = 24 cm^(2)`
Let area of parallelogram ABCD is `2y cm^(2)` and join AC.

We know that, diagonal divides the area of parallelogram in two equal areas.
`therefore` `ar (DeltaABC) = ar (ACD) = y` [say]
Also, X is the mid-point of AB.
So, `ar (DeltaACX) = ar (BCX)` [since, X is median in `DeltaABC`]
`= (1)/(2) ar (ABC) = (1)/(2)y`
Now, ar `(AXCD) = ar (DeltaADC) + ar (ACX)`
`24 = y + (y)/(2)` [given]
`rArr` `24 (3y)/(2)`
`rArr` `y = (24 xx 2)/(3) = 16 cm^(2)`
Hence, `ar (DeltaABC) = 16 cm^(2)`
Therefore, given statement is false.