8-Maths-NCERT-Exemplar-Chapter-11-Mensuration

Sep 18, 2026

UNIT 11 Mensuration summarizes key geometry measures and formulas for perimeter, area, surface areas, and volumes of common shapes. It defines perimeter and area for simple closed figures, then provides rectangle, square, triangle, parallelogram, circle, trapezium, rhombus, and cube/cuboid/cylinder area results. The solved examples practice identifying correct options, completing true statements, and computing area or volume using algebraic substitutions, scaling of dimensions, and Pythagoras-based steps. Activities also connect terminology origins such as perimeter and circumference.

LanguageEnglish

CategoryExam

FormatPDF

Pages29

Reading Time1 h 13 min

AccessFree to download

Unit 11 Mensuration

(A) Main Concepts and Results

(B) Solved Examples

Vocabulary Connections

For more FREE DOWNLOADS, visit [www.aspirationsinstitute.com](www.aspirationsinstitute.com) For more FREE DOWNLOADS, visit [www.aspirationsinstitute.com](www.aspirationsinstitute.com) UNIT 11 MENSU RATION (A) Main Concepts and Results • Length of boundary of a simple closed figure is known as perimeter. • Area is the measure of region enclosed in a simple closed curve. • Perimeter of a rectangle = 2 (length + breadth) . • Area of a rectangle = length × breadth. • Perimeter of a square = 4 × side. • Area of a square = side × side. 1 • Area of a triangle = 2 × Base × Corresponding Height. • Area of a parallelogram = Base × Corresponding Height. • Area of a circle = pr2 , where r is the radius. • Area of a trapezium = 12 × (Sum of parallel sides) × Height. • Area of a rhombus = 12 × Product of diagonals. • Lateral surface area of a cube = 4 (side)2. • Total surface area of a cube = 6 (side)2. • Lateral surface area of a cuboid = 2 × height × (length + breadth) . • Total surface area of a cuboid = 2(lb + bh + hl) . • Lateral (curved) surface area of a cylinder = 2π rh. • Total surface area of a cylinder = 2πr (r + h), where r is the radius and h is the height. For more FREE DOWNLOADS, visit [www.aspirationsinstitute.com](www.aspirationsinstitute.com) MATHEMATICS • Amount of space occupied by a solid is called its volume. • Volume of a cube = (side)3. • Volume of a cuboid = length × breadth × height. • Volume of a cylinder = πr2 h. • 1cm3 = 1ml • 1L = 1000 cm3. • 1m3 = 10,00,000 cm3 = 1,000 L. (B) Solved Examples In examples 1 and 2, there are four options out of which one is correct. Write the correct answer. Example 1 : What is the area of the triangle ADE in the following figure? A D B 8 cm C (a)45 cm2 (b) 50 cm2 (c) 55 cm2 (d) 40 cm2 Solution : The correct answer is (d) . Example 2 : What will be the change in the volume of a cube when its side becomes 10 times the original side? (a) Volume becomes 1000 times. (b) Volume becomes 10 times. (c) Volume becomes 100 times. 1 (d) Volume becomes times. 1000 Solution : The correct answer is (a) . In examples 3 and 4, fill in the blanks to make the statements true. Example 3 : Area of a rhombus is equal to ofits diagonals. Solution : Half the product. 338 EXEMPLAR PROBLEMS For more FREE DOWNLOADS, visit [www.aspirationsinstitute.com](www.aspirationsinstitute.com) UNIT-11 Example 4 : If the area of a face of a cube is 10 cm2 , then the total surface area of the cube is Solution : 60 cm2. In examples 5 and 6, state whether the statements are true (T) or false (F). Example 5 : 1L = 1000 cm3 Solution : True. Example 6 : Amount of region occupied by a solid is called its surface area. Solution : False. Example 7 : 160 m3 of water is to be used to irrigate a rectangular field whose area is 800 m2. What will be the height of the water level in the field? Solution : Volume of water = 160 m3 Area of rectangular field = 800 m2 Let h be the height of water level in the field. Now, volume of water = volume of cuboid formed on the field by water. 160 = Area of base × height = 800 × h 160 h = = 0.2 800 So, required height = 0.2 m Example 8 : Find the area of a rhombus whose one side measures 5 cm and one diagonal as 8 cm. Solution : Let ABCD be the rhombus as shown below. MENSURATION 339 For more FREE DOWNLOADS, visit [www.aspirationsinstitute.com](www.aspirationsinstitute.com) MATHEMATICS DO = OB = 4cm, since diagonals of a rhombus are perpendicular bisectors of each other. Therefore, using Pythagoras theorem in DAOB, AO2 + OB2 = AB2 AO = AB2-OB2 = 52 42 = 3 cm So, AC = 2 × 3 = 6 cm 1 1 Thus, the area of the rhombus = 2 × d1 × d2 = 2 × 8 × 6 = 24 cm2. Example 9 : The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm, find the area of the trapezium. Solution

FAQs

What is the difference between perimeter and area in Mensuration?

Perimeter is the length of the boundary of a simple closed figure. Area is the measure of the region enclosed by a simple closed curve.

How do you compute the volume of a cube and a cuboid?

The volume of a cube is (side)³, and the volume of a cuboid is length × breadth × height.

In the example where the cube’s side becomes 10 times, how does the volume change?

The volume becomes 1000 times, because volume scales with the cube of the side length.

Sep 18, 2026

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