Mensuration - (A) Main Concepts and Results - (B) Solved Examples

Sep 18, 2026

Uploaded by Callum

Mensuration notes summarize key geometric quantities, defining perimeter and area and listing essential formulas for rectangles, squares, parallelograms, circles, rhombuses, cubes, cuboids, cylinders, and conversions between volume measures like cm³, ml, and L. The material includes worked solutions and practice items that ask for areas and volumes of common shapes, apply relationships involving diagonals, Pythagoras theorem, and polygon decomposition. It also provides a strategy example on calculating painting cost for a cuboid stable partly surrounded by a cylinder.

LanguageEnglish

CategoryExam

FormatPDF

Pages28

Reading Time1 h 11 min

AccessFree to download

(A) Main Concepts and Results

Perimeter and area formulas

Volume and surface area

(B) Solved Examples

Multiple-choice area and volume questions

True/false and fill-in-the-blanks

Polygon area using decomposition

Application: painting cost strategy

MENSURATION # (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. ·Area of atn ·Area of a parallelogram =Base×Corresponding Height. ·Area of a circle =r²,where ris the radius. ·Area of a trap ·Area of a rhombu×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+h0. ·Lateral(curved)surface area of a cylinder=2πrh. ·Total surface area of a cylinder=2πr(r+h),where r is the radiusand h is the height. 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=πr²h. ·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)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 itsside becomes 10 times the original side?(a)Volume becomes 1000 times.(b)Volume becomes 10 times.(c)Volume becomes 100 times.(d)Volume becomestimes. Solution :The correct answer is(a). In examples 3 and 4,fill in the blanks to make the statements true. of its diagonals. Example 3 :Area of a rhombus is equal to_ Solution :Half the product. 12/04/18 Example 4 :If the area of a face of a cube is 10 cm²,then the totalsurface 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 surfacearea. Solution :False. Example 7 :160 m³of water is to be used to irrigate a rectangularfield whose area is 800 m².What will be the height of thewater level in the field? :Volume of water =160 m³Area 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 thefield by water. 160=Area of base×height=800×hSo,required height =0.2 m Example 8 :Find the area of a rhombus whose one side measures5 cm and one diagonal as 8 cm. Solution :Let ABCD be the rhombus as shown below. MATHEMATICS DO =OB =4cm,since diagonals of a rhombus areperpendicular bisectors of each other.Therefore,usingPythagoras theorem in △AOB,AO²+OB²=AB² AO=√AB²-OB²=√5²-4²=3cmSo,AC=2×3=6cm Thus,the area of the rhombus=24 cm². Example 9 :The parallel sides of a trapezium are 40 cm and 20 cm.Ifits non-parallel sides are both equal,each being 26 cm,find the area of the trapezium. Solution :Let ABCD be the trapezium such that AB=40 cm andCD=20 cm and AD=BC=26 cm. # Vocabulary Connections To become familiar with some of the vocabulary terms in the chapter,consider the following: 1.The square root of a number is one of the two equal factors of thenumber.For example,3 is a square root because 3×3=9.How mightpicturing plant roots help you remember the meaning of square root? 2.The word ‘perimeter’comes from the Greek roots peri,meaning ‘allaround,'and metron,meaning ‘measure.'What do the Greek roots tellyou about the perimeter of a geometric figure? 3.To square a number means ‘to multiply the number by itself,'as in2×2.Keeping this idea of square in mind,what do you think a perfectsquare might be? 4.The word 'circumference'comes from the Latin word circumferre,meaning to“carry around”.How does the Latin meaning help you definethe circumference of a circle? Now,draw CLIⅡ AD Then ALCD is a paralle

FAQs

What is the difference between perimeter and area in these notes?

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 is the volume of common solids like a cube, cuboid, and cylinder calculated?

Volume of a cube is (side)³, volume of a cuboid is length×breadth×height, and volume of a cylinder is πr²h.

How is surface area handled for a cuboid and a cylinder?

For a cuboid, lateral surface area is 2×height×(length + breadth) and total surface area is 2(lb+bh+h0) (as given). For a cylinder, lateral (curved) surface area is 2πrh and total surface area is 2πr(r+h).

How does the strategy example determine the painting cost of the stable?

The approach computes the paintable area on the cylinder top and the cuboid walls, adds both to get total area, then multiplies by the given rate Rs 2 per m².

Sep 18, 2026

Uploaded by Callum