Question

1. fill - in - the - blank. as shown in the figure, (ab = 4bd). given that the area of triangle (abc) is (36mathrm{cm}^2), then the area of triangle (bcd) is (mathrm{cm}^2).

Explanation:

Step1: Analyze the relationship of bases

Triangles $ABC$ and $BCD$ have the same height (the perpendicular distance from $C$ to $AD$). Let the height of both triangles be $h$. The base of $\triangle ABC$ is $AB$ and the base of $\triangle BCD$ is $BD$. Given $AB = 4BD$.

Step2: Use the triangle - area formula

The area formula of a triangle is $S=\frac{1}{2}\times base\times height$. The area of $\triangle ABC$, $S_{ABC}=\frac{1}{2}\times AB\times h = 36\ cm^{2}$. The area of $\triangle BCD$, $S_{BCD}=\frac{1}{2}\times BD\times h$. Since $AB = 4BD$, we can rewrite $S_{ABC}=\frac{1}{2}\times4BD\times h = 36\ cm^{2}$, then $\frac{1}{2}\times BD\times h=\frac{36}{4}$.

Answer:

9