Question

What is the area of $\triangle ABC$ (in square cm) if $AD$ is the median and area $\triangle ADB = 18$ square cm? (A) 36 (B) 18 square cm (C) 9 square cm (D) 12 square cm

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Answer

The correct option is (A) 36.

A median of a triangle divides the triangle into two triangles of equal area. Given that $AD$ is the median of $\triangle ABC$, it divides $\triangle ABC$ into two smaller triangles: $\triangle ADB$ and $\triangle ADC$.

Since the area of $\triangle ADB$ is 18 square cm, the area of $\triangle ADC$ will also be 18 square cm.

Therefore, the total area of $\triangle ABC$ can be calculated as follows:

$$ \text{Area of } \triangle ABC = 2 \times \text{Area of } \triangle ADB = 2 \times 18 = 36 \text{ square cm} $$

Thus, the area of $\triangle ABC$ is 36 square cm.

Therefore, the correct answer is (A) 36.


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