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# 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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