**Area of shaded region :**

Here we are going to see some examples of finding area of shaded region.

Procedure of finding area of shaded region will change problem to problem.

**Example 1 :**

Find the area of the shaded portion

**Solution :**

To find the area of shaded portion of given composite figure, first let us draw a line

Area of given figure = Area of ABGE + Area of GCFD

**Area of ABGE :**

Area of rectangle = Length ⋅ Width

length BE = 6 m, width GE = 2 m

Area of ABGE = 6(2) = 12 m^{2}

**Area of GCFD :**

Area of rectangle = Length ⋅ Width

length CD = 6 m, width FD = 2 m

Area of GCFD = 6(2) = 12 m^{2}

Area of shaded portion = 12 + 12 = 24 m^{2}

**Example 2 :**

Find the area of the shaded portion

**Solution :**

To find the area of shaded portion, we have to subtract area of GEHF from area of rectangle ABCD.

Area of shaded portion

= Area of rectangle ABCD - Area of square GEHF

**Area of ABCD :**

Area of rectangle = Length ⋅ Width

Length AB = 20 cm

Width AC = 16 cm

Area of ABCD = 20 (16) = 320 cm^{2}

**Area of GEHF :**

Area of square (GEHF) = side ⋅ side

Length GE = 6 cm

Area of square GEHF = 6 ⋅ 6

Area of square (GEHF) = 36 cm^{2}

Area of shaded region = 320 - 36 = 284 cm^{2}

**Example 3 :**

Find the area of the shaded portion

**Solution :**

To find the area of shaded region, we have to subtract area of semicircle with diameter CB from area of semicircle with diameter AB and add the area of semicircle of diameter AC.

Area of shaded portion

= Area of AEB - Area of semicircle with diameter BC + area of semicircle with diameter AC

Area of semicircle AEB = (1/2) Πr^{2}

= (1/2) **⋅** (22/7) **⋅** (14)^{2}

= (1/2) **⋅** (22/7) **⋅** 14 **⋅** 14

= 22 **⋅** 14

= 308 cm^{2}

**Example 4 :**

Find the area of the shaded region

**Solution :**

To find the area of shaded portion, we have to subtract area of semicircles of diameter AB and CD from the area of square ABCD.

Area of shaded portion

= Area of square ABCD - (Area of semicircle AEB + Area of semicircle DEC)

= a^{2} - [ (1/2) Πr^{2}) + ((1/2) Πr^{2}) ]

= 7^{2} - Πr^{2}

= 49 - (22/7) **⋅** (7/2)^{2}

= 49 - (22/7) **⋅** (7/2) **⋅** (7/2)

= 49 - 38.5

= 10.5 cm^{2}

Related Topics

- perimeter of sector
- Length of arc
- Practice questions on length of arc
- Perimeter of square
- Perimeter of parallelogram
- Perimeter of rectangle
- Perimeter of triangle
- Area of a circle
- Area of Semicircle
- Area of Quadrant
- Area of sector
- Area of triangle
- Area of equilateral triangle
- Area of scalene triangle
- Area of square
- Area of rectangle
- Area of parallelogram
- Area of rhombus
- Area of trapezium
- Area of quadrilateral
- Area around circle
- Area of pathways
- Area of combined shapes

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