FIND AREA OF SHADED COMPOSITE FIGURES

Work out the shaded area.

Problem 1 :

Solution :

Shaded area = Area of large rectangle – area of small rectangle

= (9 × 5) – (4 × 3)

= 45 – 12

= 33 cm²

So, shaded area is 33 cm².

Problem 2 :

Solution :

Shaded area

= Area of large rectangle - area of small rectangle

length of large rectangle = 10 cm, width = 12 cm

length of small rectangle = 10 - 2.5 - 2.5 ==> 5 cm

Width of the small rectangle = 12 - 1 - 1 ==> 10 cm

= (10 x 12) - (5 x 10)

= 120 - 50

= 70 cm²

Problem 3 :

Solution :

Shaded area

= Area of square – Area of large rectangle - Area of small rectangle

= (15)² – (8 × 3) – (2 × 3)

= 225 – 24 – 6

= 195 cm²

So, shaded area is 195 cm².

Shown is a triangular brick wall with a rectangular window. Find the area of the wall that is brick.

Problem 4 :

Solution :

Area of the wall = area of a triangle – area of rectangle

= (1/2) (b × h) - (l × w)

= (1/2) (6 × 7) – (1.5 × 2)

= 1/2 (42) – 3

= 21 – 3

= 18 m²

So, area of the wall is 18 m².

Find the area of the garden that is grass.

Problem 5 :

Solution :

The area of the garden = area of square - area of triangle

= a² – 1/2 (b × h)

= 6² – 1/2 (4 × 3)

= 36 – 1/2 (12)

= 36 – 6

= 30 m²

So, area of the garden is 30 m².