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1 Perimeter of a closed figure is the distance around it while area isthe measure of the part of plane or region enclosed by it. Perimeter of a regular polygon = Number of sides Length of oneside. Perimeter of a square = 4 sideFig. Perimeter of a rectangle = 2(l + b)Fig. area of square = side side area of rectangle = l b area of parallelogram = b h area of triangle = 12b h Fig. Fig. The distance around a circle is known as its circumference. The ratio of circumference and diameter of a circle is a constant andis denoted by (pi). Approximate value of is taken as 227 or Circumference of a circle of radius r is 2 r, area of a circle of radius r is In Examples 1 and 2, there are four options, out of which one is the correct 1:Following rectangle is composed of 8 congruent WordsNumbersFormulaThe circumference C ofa circle is times thediameter d, or 2 times the radius 6=2 3= unitsC= dorC=2 r15-04-2018 area of each part is(a) 72 cm2(b) 36 cm2(c) 18 cm2(d) 9 cm2 Solution:Correct answer is (d).

2 Example 2: area of a right triangle is 54 cm2. If one of its legs is12 cm long, its perimeter is(a) 18 cm(b) 27 cm(c) 36 cm(d) 54 cmFig. :Correct answer is (c).In Examples 3 to 6, fill in the blanks tomake it a statement 3: area of parallelogramQPON is :48 cm2 WordsNumbersFormulaThe area A of a circleis times the squareof the radius 32=9 = unitsA= r2 Fig. Example 4:1 hectare = cm2 Solution:10,00,00,000 Example 5: squares of each side 1 m makes a square of side5 :2,50,00,000 Example 6:All the congruent triangles have :equalIn Examples 7 to 10, state whether the statements are True or 7:All the triangles equal in area are :FalseExample 8:The area of any parallelogram ABCD, is AB 9:Ratio of the circumference and the diameter of a circle ismore than :TrueExample 10:A nursery school play ground is 160m long and 80mwide.

3 In it 80m 80m is kept for swings and in theremaining portion, there is wide path parallel toits width and parallel to its remaining length as shownin Fig. The remaining area is covered by grass. Findthe area covered by Solution : area of school playground is 160m 80 m = 12800 m2 area kept for swings = 80m 80m = 6400 m2 area of path parallel to the width of playground= 80m m = 120 m2 area of path parallel to the remaining length ofplayground= 80m m = 120 common to both paths = m = m2.[since it is taken twice for measuerment it is to besubtracted from the area of paths]Total area covered by both the paths= (120 + 120 ) m2= covered by grass= area of school playground (Areakept for swings + area covered by paths)= 12800 m2 [ 6400 + ] m2= (12800 )m2= side of a triangle can be the base.

4 The diagrams below show thelength of the base (b) and the height (h) of several represents thelength of the represents Example 11:In Fig. , ABCD is a parallelogram, in whichAB = 8cm, AD = 6cm and altitude AE = 4cm. Find thealtitude corresponding to side : area of parallelogram ABCD = AB AE = 8 4 cm2= 32 cm2 Let altitude corresponding to AD be h. Then,h AD = 32orh 6 = 32orh = 321663=Thus, altitude corresponding to AD is 163 12:A rectangular shaped swimming pool with dimensions30 m 20 m has 5 m wide cemented path along itslength and 8 m wide path along its width (as shown inFig. ). Find the cost of cementing the path at therate of Rs 200 per m2. Fig. Solution: area covered by swimming pool = 30m 20 m= 600 of outer rectangle = (30 + 8 + 8) m = 46 mand its breadth = (20 + 5 + 5) m = 30 mSo, the area of outer rectangle = 46m 30 m = 1380 of cemented path = area of outer rectangle area of swimming pool = (1380 600) m2 = 780 of cementing 1 m2 path = 200So, total cost of cementing the path = 780 200 = 156000 To become familiar with some of the vocabulary termsconsider the word circumference contains the prefix circum-,which means around.

5 What do you think about thecircumference of a circle? Greek prefix peri- means around, and the rootmeter means means of measuring. What do yousuppose perimeter means? Greek prefix dia- means across. What do youthink about the diameter of a circle?Example 13:Circumference of a circle is 33cm. Find its :Let the radius of the circle be ,2 r = 3315-04-2018 , r = = =333372122224 Thus, radius is 214cmSo, area of the circle = = = 6938 Thus, area of the circle is 14:Rectangle ABCD is formed in acircle as shown in Fig. If AE= 8 cm and AD = 5 cm, find theperimeter of the :DE=EA + AD =(8 + 5)cm =13 cmDE is the radius of the , DB is the radius ofthe , AC = DB [Since diagonals of a rectangle are equalin length]Therefore, AC = 13 ADC, DC2 = AC2 AD2 = 132 52 = 169 25 =144 = 122So, DC = 12 Thus, length of DC is 12 , perimeter of the rectangle ABCD= 2 (12 + 5)cm = 34 15 Find the area of a parallelogram shaped shaded regionof Fig.

6 Also, find the area of each triangle. Whatis the ratio of area of shaded portion to the remainingarea of rectangle?Fig. Fig. : Understand and Explore the Problem What information is given in the question?(i)It is given that ABCD is a rectangle whose l = 10 cmand b = 6 cm.(ii)In the figure AF = 4cm(iii)To find the area of shaded region. Plan a Strategy First recall the areas of a triangle and a rectangleArea of a rectangle = length breadthArea of a triangle = 12 base altitude In the Fig. , DAF is a right triangle in which A = 90 .ABCD is a rectangle and DEBF is a parallelogram,Since DAF BCE, therefore their areas will be equal. Solve area of DAF = 2146cm2 15-04-2018 In the Questions 1 to 37, there are four options, out of which one iscorrect.

7 Choose the correct the shapes 1, 2, 3 and 4 in the figures. Which of the followingstatements is not correct? area of rectangle = l b= 10 cm 6 cm = 60 cm2 area of shaded region = area of rectangle area of DAF area of BCE = (60 12 12)cm2= (60 24)cm2 = 36 cm2 area of remaining part = area of Rectangle area ofshaded portion= (60 36)cm2 = 24 cm2 Ratio = area of shaded portion : area of remaining rectangle = 36 : 24 = 3 : 2 Revise area of shaded portion + area of remaining portion = area of rectangleThat is, (36 + 24)cm2 = 60 cm2 can also calculate area of shaded portion by using area ofparallelogram. Think what would be its base and you frame, questions in which areas of all the plane figuresrectangle, square, triangle and a parallelogram are to be calculated?

8 15-04-2018 (a)Shapes 1, 3 and 4 have different areas and different perimeters.(b)Shapes 1 and 4 have the same area as well as the same perimeter.(c)Shapes 1, 2 and 4 have the same area .(d)Shapes 1, 3 and 4 have the same rectangular piece of dimensions 3cm 2cm was cut from arectangular sheet of paper of dimensions 6cm 5cm (Fig. ). area of remaining sheet of paper isFig. (a)30 cm2(b) 36 cm2 (c) 24 cm2 (d)22 cm2 the area of a rectangle with base b and height h with thearea of a rectangle with base 2b and height the formulas for the area and perimeter of a square usings for the length of a unit squares are joined to form a rectangle with the least of the rectangle is(a) 12 units(b) 26 units(c) 24 units(d) 36 wire is bent to form a square of side 22cm.

9 If the wire is rebent toform a circle, its radius is(a)22 cm(b)14 cm(c)11 cm(d)7 of the circle obtained in Question 4 is(a)196 cm2(b)212 cm2(c)616 cm2(d)644 of a rectangle and the area of a circle are equal. If the dimensionsof the rectangle are 14cm 11 cm, then radius of the circle is(a)21 cm(b) cm(c)14 cm (d)7 of shaded portion in Fig. is(a)25 cm2(b)15 cm2(c)14 cm2 (d)10 cm2 Fig. of parallelogram ABCD (Fig. ) is not equal to(a) DE DC(b) BE AD(c) BF DC (d) BE BC the formula for the area of a circle in terms of the diameter Fig. of triangle MNO of Fig. isFig. (a) 12 MN NO(b) 12 NO MO (c) 12 MN OQ (d) 12 NO of area of MNO to the area of parallelogram MNOP in thesame figure is(a)2 : 3(b)1 : 1(c)1 : 2(d)2 : of areas of MNO, MOP and MPQ in Fig.

10 Is(a)2 : 1 : 3(b)1 : 3 : 2(c) 2 : 3 : 1 (d) 1 : 2 : 3 what happens to the area of a triangle when the base isdoubled and the height remains the what happens to the area of a parallelogram when the lengthof its base is doubled but the height remains the Fig. Fig. , EFGH is aparallelogram, altitudes FKand FI are 8 cm and 4cmrespectively. If EF = 10 cm,then area of EFGH is(a) 20 cm2 (b) 32 cm2(c) 40 cm2 (d) 80 cm2 The Taj Mahal, a world famous structure, is the most visited attraction inIndia. It was created in the 17th century by Emperor Shah Jahan to honourthe memory of his beloved wife Mumtaz Mahal. The design of the Taj Mahalis based on the number four and its about garden at the Taj Mahal was laid out in four squares of the samesize. Each square was divided into four flower beds, with 400 flowersin each bed.