Perimeter of combined figures

Recap - Shape and Formula Shapes Perimeter formula Square Perimeter of Square(P) = 4 x S S- Side length. Rectangle Perimeter of Rectangle (P) = 2 ( l + b ) l - Length and b - breadth Triangle Perimeter of triangle (P) = sum of 3 sides P = a + b + c a, b and c are length of sides

Shapes Perimeter formula Circle Perimeter of circle(P) = 2πr r - radius of circle Semicircle Perimeter of Semicircle (P) =πr+2r r - radius of circle Quadrant circle Perimeter of Quadrant circle (P) =

Examples for Perimeter Questions Answers Perimeter of Square P = ? Perimeter of Square (P)=4 x S P = 4 X 5 (S=5cm) Ans: P = 20 cm Perimeter of Rectangle P = ? Perimeter of Rectangle (P) = 2(l+b) P = 2 (7 + 4 ) (l=7cm, b=4cm) P = 2 * 11 Ans: P = 22 cm Perimeter of Triangle P= ? Perimeter of triangle (P) = sum of 3 sides P = 3 + 4 + 5 Ans : P = 12 cm

Questions Answers Perimeter of Circle P = ? Perimeter of circle (P) = 2πr Given, r = 4 P = 2 * 3.14 + 4 (π = 3.14, r =4 ) P = 6. 28 + 4 Ans: P = 10 . 28 cm Perimeter of Semicircle (P) = πr+2r Given d=6 ,  r=d/2= 6/2= 3 P = 3.14 * 3 + 2 *3 (π = 3.14,r=3 ) P = 9.42 + 6 Ans: P=15.42 cm Perimeter of Semicircle P=? Perimeter of Quadrant circle P=? Perimeter of Quadrant circle (P) = Given r = 2 P= P= 3.14 + 4 Ans: P= 6.14

Example 1: Find the perimeter of the following Combined figure. Solution: We know perimeter of combined shapes is the sum of all the outer sides Step 1: Find all the missing sides Given BC=4cm,CD=8cm and AE=DE=AD From the figure we can see ABCD is a rectangle ∴ BC=AD= 4cm and CD=AB=8cm (∵ In a rectangle length and breath are same) ∴ AE=4cm , DE=4m (Given AE=DE=AD) Step 2: Perimeter of Combined figure = sum of all the outer side = AB + BC + CD + DE + EA = 8 + 4 + 8 + 4 + 4 = 28 cm Ans : Perimeter of Combined figure = 28 cm

Example 2: Find the perimeter of the following Combined figure. Solution: We know perimeter of combined shapes is the sum, of all the outer sides Step 1: Find all the missing sides Given, Side of triangle AB = 5 cm, AD= 4 cm and BD = 6 cm From the figure we can see BCD is a semicircle. we need to find length of arc Step 2 : length of = πr Given d=6cm (BD)  r = d/2 = 6/2= 3 cm length of = (π= and r=3) length of (By using Perimeter of semi circle formula ) (Given radius value)

Step 3: Perimeter of Combined figure = sum of all the outer side = AB + + DA = 5 + 9.4 + 4 Ans : Perimeter of Combined figure = 18.4 m

Example 3 : Find the perimeter of the following combined figure. Solution: We know perimeter of combined shapes is the sum of all the outer sides Step 1: Find all the missing side From the figure we can see BCEF is a rectangle Given, side of rectangle BC = EF = 12 cm and BF= CE= 7 cm (∵ In a rectangle length and breadth are same). From the figure we can see BAF and CDE is a quadrant. AB=BF= 7 cm and CD=CE= 7 cm. (∵ radius of quadrant r = 7 cm) we need to find length of arc and . We need apply the quadrant formula.

Step 2 : length of = (π= and r=7) By using Perimeter of quadrant formula Step 3: Perimeter of Combined figure = sum of all the outer side = AB + BC + CD + + EF + = 7 + 12 + 7 + 11 + 12 + 11 Ans : Perimeter of Combined figure = 60 cm

Try these 1. Find the perimeter of the following Combined figure.