FINDING AREA OF COMPOUND SHAPES

Work out the area of each of these shapes.

Problem 1 :

Solution :

Area of shape given = Area of rectangle + area of rectangle

Area of the rectangle = length x width

= (9 × 8) + (7 × 5)

= 72 + 35

= 107 cm²

Problem 2 :

Solution :

Required area

= Area of large rectangle + area of small rectangle

= (25 × 12) + (6 × 10)

= 300 + 60

= 360 cm²

Problem 3 :

Solution :

Required area

= Area of rectangle at the bottom + area of rectangle at the top

= (4 × 7) + (13 × 3)

= 28 + 39

= 67 cm²

Problem 4 :

Solution :

Required area

= Area of rectangle at the bottom + area of rectangle at the top

= (9 × 3) + (2 × 5)

= 27 + 10

= 37 cm²

Problem 5 :

Solution :

Required area

= Area of large rectangle + area of 3 small rectangles 

= (24 × 8) + (6 × 12) + (6 × 12) + (2 × 12)

= 192 + 72 + 72 + 24

= 360 cm²

Problem 6 :

Solution :

Required area

= Area of large rectangle + area of 2 small rectangles

= (8 × 4) + (2 × 3) + (3 × 3)

= 32 + 6 + 9

= 47 cm²

Problem 7 :

Solution :

Area of required shape

= Area of rectangle + area of 3 rectangles

= (3 × 8) + (7 × 4) + (16 × 2)

= 24 + 28 + 32

= 84 cm²

Problem 8 :

Solution :

Area of the required shape

= Area of rectangle + area of rectangle

= (20 × 7) + (7 × 9)

= 140 + 63

= 203 cm²

Problem 9 :

Solution :

Area of the required shape

= Area of rectangle + area of rectangle + area of rectangle

= (5 × 7) + (4 × 2) + (5 × 7)

= 35 + 8 + 35

= 78 cm²