Area of combined figures

Recap - Formula of known shapes Shapes Area formula Square Area of Square(A) = S x S S- Side length. Rectangle Area of Rectangle (A) = l * b l - Length and b - breadth Triangle Area of triangle (A) = b-base and h- height

Recap - Formula of known shapes Shapes Area formula Circle Area of circle(A) = πr2 r - radius of circle Semi circle Area of Semicircle (A) = r - radius of semi circle Quadrant circle Area of Quadrant circle (A) = r - radius of quadrant circle

Examples for Area of known shapes Questions Answers Area of Square A = ? Area of Square (A)= S x S A = 5 X 5 (S=5cm) Ans: A = 25 cm2 Area of Rectangle A = ? Area of Rectangle (A) =l x b A = 4 x 7 (l=7cm, b=4cm) Ans: A = 28 cm2 Area of Triangle A= ? Area of triangle (A) = Ans : A = 6 cm2

Recap - Formula of known shapes Questions Answers Area of Circle A = ? Area of circle (A) = πr2 Given, r = 4 A = 3.14 * 4 * 4 (π = 3.14, r =4 ) Ans: A = 50.24 cm2 Area of Semicircle (A) = Given d=6 ,  r=d/2= 6/2= 3 Ans: A=14.13 cm2 Area of Semicircle A=? Area of Quadrant circle A=? Area of Quadrant circle (A) = Given r = 2 Ans: A= 3.14 cm2

Example 1: Find the Area of the following Combined figure. Solution: Step 1: Split the combined shape into known figures From the above figure we can see that ABCD is a rectangle and ADE is a triangle. Step 2: Find area of know figure Area of ▭ABCD = l x b = 8 x 4=32 Area of ∆ADE= (BC=AD=4, l=4, h=4) Step 3:- Area of Combined figure = sum of all known figures = Area of ▭ABCD + Area of ∆ADE = 32 + 8 = 40 cm2 Ans : Area of Combined figure = 40 cm2

Example 2: Find the Area of the following Combined figure. Solution: Step 1: Split the combined shape into known figures From the above figure we can see that ABD is a triangle and BCD is a semi circle. Step 2: Find area of known figure Area of ∆ABD= (b=6, h=4) Area of BCD= BD = diameter = 6cm ; r = d/2 = 6/2 = 3cm) Step 3:- Area of Combined figure = sum of all known figures = Area of ∆ABD + Area of BCD = 12 + 14.13 = 26.13 cm2 Ans : Area of Combined figure = 26.13 cm2

Example 3 : Find the area of the following combined figure. Solution: We know area of combined shapes is the sum of all the outer sides Step 1: Split the combined shape into known figures 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 both length or both 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)

Cont…. Step 2 : Find area of known figure Area of ▭BCEF = l x b = 12 x 7 = 84 Area of BAF + Area of CDE = = 38.465 + 38.465 = 76.93 Step 3: Area of Combined figure = sum of all known figures = Area of ▭BCEF + Area of BAF + Area of CDE = 84 + 76.93 = 160.93 Ans : Area of Combined figure = 160.93 cm2

Try these… 1. Find the area of the following Combined figure.