Question : $ABC$ is a triangle. $AB = 5$ cm, $AC = \sqrt{41}$ cm and $BC = 8$ cm. $AD$ is perpendicular to $BC$. What is the area (in cm²) of $\triangle ABD$?

Question : If $\triangle ABC \sim \triangle PQR$, AB =4 cm, PQ=6 cm, QR=9 cm and RP =12 cm, then find the perimeter of $\triangle$ ABC.

Question : $\triangle$ABC is similar to $\triangle$DEF. If the area of $\triangle$ABC is 9 sq. cm and the area of $\triangle$DEF is 16 sq. cm and BC = 2.1 cm, then the length of EF will be:

Question : Suppose $\triangle ABC$ be a right-angled triangle where $\angle A=90°$ and $AD\perp BC$. If the area of $\triangle ABC =40$ cm$^{2}$ and $\triangle ACD =10$ cm$^{2}$ and $\overline{AC}=9$ cm, then the length of $BC$ is:

Question : Let A, B, and C be the mid-points of sides PQ, QR, and PR, respectively, of PQR. If the area of $\triangle$ PQR is 32 cm², then find the area of $\triangle$ ABC.