1. Area of combined figures

2. 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

3. 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

4. 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

5. Recap - Formula of known shapes
Questions Answers
Area of Circle A = ?
Area of circle (A) = πr2
Given, r = 4
A = 3.14 * 4 * (π = 3.14, r =4 )
Ans: A = 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

6. 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 =
= 40 cm2
Ans : Area of Combined figure = 40 cm2

7. 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 =
= cm2
Ans : Area of Combined figure = cm2

8. 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)

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

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