Prepared by Muhammad Tayyab, Subject Specialist Mathematics, Govt Christian High School Daska
📌 Based on National Curriculum / PECTA 2025 Syllabus
📖 What's Inside: This MCQ set covers properties of similar figures, area and volume ratios, and geometric properties of polygons. Perfect for Punjab Boards exam preparation.
📚 Related Resources – Chapter 9: Similar Figures
1
If two polygons are similar, then:
A) their corresponding angles are equal. ✔
B) their areas are equal.
C) their volumes are equal.
D) their corresponding sides are equal.
Similar polygons have corresponding angles equal and corresponding sides proportional.
2
The ratio of the areas of two similar polygons is:
A) equal to the ratio of their perimeters.
B) equal to the square of the ratio of their corresponding sides. ✔
C) equal to the cube of the ratio of their corresponding sides.
D) equal to the sum of their corresponding sides.
The area ratio of similar polygons is the square of the ratio of their corresponding sides.
3
If the volume of two similar solids is \(125\text{ cm}^3\) and \(27\text{ cm}^3\), the ratio of their corresponding heights is:
A) \(3:5\) ✔
B) \(5:3\)
C) \(25:9\)
D) \(9:25\)
\[\frac{V_1}{V_2} = \left(\frac{l_1}{l_2}\right)^3\]
\[\frac{125}{27} = \left(\frac{l_1}{l_2}\right)^3\]
\[\sqrt[3]{\frac{125}{27}} = \frac{l_1}{l_2} = \frac{5}{3}\]
Ratio of heights = \(5:3\)
4
The exterior angle of a regular pentagon is:
A) \(40^\circ\)
B) \(45^\circ\)
C) \(60^\circ\)
D) \(72^\circ\) ✔
\[\text{Exterior angle} = \frac{360^\circ}{5} = 72^\circ\]
\(72^\circ\)
5
A parallelogram has an area of \(64\text{ cm}^2\) and a similar parallelogram has an area of \(144\text{ cm}^2\). If a side of the smaller parallelogram is \(8\text{ cm}\), the corresponding side of the larger parallelogram is:
A) \(10\text{ cm}\)
B) \(12\text{ cm}\) ✔
C) \(18\text{ cm}\)
D) \(16\text{ cm}\)
\[\frac{A_1}{A_2} = \left(\frac{l_1}{l_2}\right)^2\]
\[\frac{64}{144} = \left(\frac{8}{l_2}\right)^2\]
\[\frac{8}{12} = \frac{8}{l_2} \Rightarrow l_2 = 12\text{ cm}\]
\(12\text{ cm}\)
6
The total number of diagonals in a polygon with \(9\) sides is:
A) \(18\)
B) \(21\)
C) \(25\)
D) \(27\) ✔
\[\text{Diagonals} = \frac{n(n-3)}{2} = \frac{9(9-3)}{2} = \frac{54}{2} = 27\]
\(27\) diagonals
7
Two spheres are similar, and their radii are in the ratio \(4:5\). If the surface area of the larger sphere is \(500\pi\text{ cm}^2\), what is the surface area of the smaller sphere?
A) \(256\pi\text{ cm}^2\)
B) \(320\pi\text{ cm}^2\) ✔
C) \(400\pi\text{ cm}^2\)
D) \(405\pi\text{ cm}^2\)
\[\frac{A_1}{A_2} = \left(\frac{r_1}{r_2}\right)^2\]
\[\frac{A_1}{500\pi} = \left(\frac{4}{5}\right)^2 = \frac{16}{25}\]
\[A_1 = \frac{16 \times 500\pi}{25} = 320\pi\text{ cm}^2\]
\(320\pi\text{ cm}^2\)
8
A regular polygon has an exterior angle of \(30^\circ\). How many diagonals does the polygon have?
A) \(54\) ✔
B) \(90\)
C) \(72\)
D) \(108\)
\[\text{Exterior angle} = \frac{360^\circ}{n} \Rightarrow 30^\circ = \frac{360^\circ}{n} \Rightarrow n = 12\]
\[\text{Diagonals} = \frac{12(12-3)}{2} = \frac{108}{2} = 54\]
\(54\) diagonals
9
In a regular hexagon, the ratio of the length of a diagonal to the side length is:
A) \(\sqrt{3}:1\)
B) \(2:1\) ✔
C) \(3:2\)
D) \(2:3\)
In a regular hexagon, the longest diagonal connects opposite vertices and is twice the side length, so the ratio is \(2:1\).
10
A regular polygon has an interior angle of \(165^\circ\). How many sides does it have?
A) \(15\)
B) \(16\)
C) \(20\)
D) \(24\) ✔
\[\text{Exterior angle} = 180^\circ - 165^\circ = 15^\circ\]
\[15^\circ = \frac{360^\circ}{n} \Rightarrow n = \frac{360^\circ}{15^\circ} = 24\]
\(24\) sides
📈 Key Concepts – Similar Figures
- Similar Figures: Same shape, different size. Corresponding angles are equal, corresponding sides are proportional.
- Scale Factor: Ratio of corresponding sides. Used to enlarge or reduce figures.
- Area Ratio: Ratio of areas = (scale factor)².
- Volume Ratio: Ratio of volumes = (scale factor)³.
- Regular Polygons: Exterior angle = 360°/n, Interior angle = 180°(n-2)/n.