ABCD is a parallelogram and X is the mid-point of AB. If ar (AXCD) = 24 cm², then ar (ABC) = 24 cm². Is the given statement true or false and justify your answer.
Solution:
It is given that
ABCD is a parallelogram
ar (AXCD) = 24 cm²
Consider area of parallelogram ABCD as 2y cm² and join AC
As the diagonal divides a parallelogram into two equal areas
Consider ar (∆ ABC) = ar (ACD) = y
X is the midpoint of AB
As X is the median in ∆ ABC
ar (∆ ACX) = ar (BCX)
= 1/2 ar (ABC)
= 1/2 y
We know that
ar (AXCD) = ar (∆ ADC) + ar (ACX)
As ar (∆ ACX) = 1/2 y
24 = y + y/2
Taking LCM
24 = 3y/ 2
y = (24 x 2)/ 3
y = 16 cm²
So ar(ABC) = 16 cm²
Therefore, the statement is false.
✦ Try This: ABCD is a parallelogram and X is the mid-point of AB. If ar (AXCD) = 14 cm², then what is the ar (ABC)?
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 9
NCERT Exemplar Class 9 Maths Exercise 9.2 Problem 1
ABCD is a parallelogram and X is the mid-point of AB. If ar (AXCD) = 24 cm², then ar (ABC) = 24 cm². Is the given statement true or false and justify your answer.
Summary:
The statement “ABCD is a parallelogram and X is the mid-point of AB. If ar (AXCD) = 24 cm², then ar (ABC) = 24 cm²” is false
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