Note: This is the Solution of review exercise 9.2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 9.2
Question # 01: Find the ratio of the areas of similar figures if the ratio of their corresponding lengths are:
\((i) \quad \) \(1:3\)
\((ii) \quad \) \(3:4\)
\((iii) \quad \) \(2:7\)
\((iv) \quad \) \(8:9\)
\((v) \quad \) \(6:5\)
Question 2: Find the unknowns in the following figures:
Question 3: Given that area of \(\small{\triangle ABC=36\ cm^2}\) and \(\small{m\overline{AB}=6\ cm}\), \(\small{m\overline{BD}=4\ cm}\). Find
\( (a) \; \) the area of \(\triangle ADE\)
\( (b) \; \) the area of trapezium \(BCED\)
Question 4: Given that \(\small{\triangle ABC}\) and \(\small{\triangle DEF}\) are similar, with a scale factor of \(\small{k=3}\). If the area of \(\small{\triangle ABC}\) is \(\small{50\ cm^2}\), find the area of \(\small{\triangle DEF}\)?
Question 5: Quadrilaterals \(\small{ABCD}\) and \(\small{EFGH}\) are similar, with a scale factor of \(\small{k=} \frac{1}{4}\). If the area of quadrilateral \(\small{ABCD}\) is \(\small{64\ cm^2}\), find the area of quadrilateral \(\small{EFGH}\).
Question 6: The areas of two similar triangles are \(\small{16\ cm^2}\) and \(\small{25\ cm^2}\). What is the ratio of a pair of corresponding sides.
Question 7: The areas of two similar triangles are \(\small{144\ cm^2}\) and \(\small{81\ cm^2}\). If the base of the large triangle is \(\small{30\ cm}\), find the corresponding base of the smaller triangle.
Question 8: A regular heptagon is inscribed in a larger regular heptagon and each side of the larger heptagon is \(\small{1.7}\) times the side of the smaller heptagon. If the area of teh smaller heptagone is known to be \(\small{100\ cm^2}\), find the area of the larger heptagon.
