# 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

## 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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