AREA OF SHADED SHAPE IN GRID

Find the area of each shaded section. Each block is 1 square unit (u).

Problem 1 :

Solution :

Total number of complete squares = 40

= 40 × 1

Area of compete squares = 40

Total number of half squares = 9

= 9 × 0.5

Area of half squares = 4.5

Area of shaded section = 40 + 4.5

= 45 units²

So, area of shaded shape is 45 units². 

Problem 2 :

Solution :

By observing the figure,

Total number of complete squares = 34

= 34 × 1

Area of complete squares = 34

Total number of half squares = 16

= 16 × 0.5

Are of half squares = 8

Area of shaded section = 34 + 8

= 42 units²

So, area of shaded section is 42 units².

Problem 3 :

Solution :

Total number of complete squares = 8

= 8 × 1

Area of complete squares = 8

Total number of half squares = 4

= 4 × 0.5

Area of half squares = 2

Area of shaded section = 8 + 2

= 10 units²

So, area of shaded section is 10 units².

Problem 4 :

Solution :

Total number of complete squares = 42

= 42 × 1

= 42

Total number of half squares = 14

= 14 × 0.5

= 7

Area of shaded section = 42 + 7

= 49 units²

So, area of shaded section is 49 units².

Problem 5 :

Solution :

Total number of complete squares = 29

= 29 × 1

= 29

Total number of half squares = 12

= 12 × 0.5

= 6

Area of shaded section = 29 + 6

= 35 units²

So, area of shaded section is 35 units².

Problem 6 :

Solution :

Total number of complete squares = 44

= 44 × 1

= 44 units

Total number of half squares = 8

= 8 × 0.5

= 4 units

Area of shaded section = 44 + 4

= 48 units²

So, area of shaded section is 48 units².

Problem 7 :

Solution :

By observing the figure,

Total number of complete squares = 44

= 44 × 1

= 44 units

Total number of half squares = 4

= 4 × 0.5

= 2 units

Area of shaded section = 44 + 2

= 46 units²

So, Area of shaded section is 46 units².

Problem 8 :

Solution :

Total number of complete squares = 21

= 21 × 1

= 21

Total number of half squares = 6

= 6 × 0.5

= 3

Area of shaded section = 21 + 3

= 24 units²

So, area of shaded section is 24 units².

Each square on the grid paper is 1 square inch. Find the area of the figure.

Problem 9 :

Solution :

Decomposing the shape into two parts, one part is a rectangle and another part is a trapezium.

About rectangle :

Length = 5 units and width = 3 units

Area of rectangle = length x width

= 5 x 3

= 15 square units

About trapezium :

height = 3, lengths of paralel sides = 6 units and 3 units.

Area of trapezium = (1/2) x height x sum of length of parallel sides

= (1/2) x 3 x (6 + 3)

= 1.5 x 9

= 13.5 square units

Problem 10 :

Solution :

Total area in the grid above = 2 (area of trapezum)

= 2 x 1/2 x height x sum of length of parallel sides

height = 3 units, lenghts of parallel sides = 4 units and 7 units 

= 2 x (1/2) x 3 x (4 + 7)

= 3 x 11

= 33 square units.

Problem 11 :

Solution :

Total area in the grid above = Area of triangle + area of trapezium

About triangle :

Base = 6 units and height = 3 units

About trapezium :

height = 4 units, lengths of bases = 2 units and 6 units

Area in the grid = (1/2) x 6 x 3 + (1/2) x 4 x (2 + 6)

= 9 + 2 x 8

= 9 + 16

= 25 square units.

Problem 12 :

Solution :

Area of shaded region = area of rectangle + area of parallelogram

length = 5 units and width = 3 units

base of parallelogram = 5 units and height = 3 units

= 5 x 3 + 5 x 3

= 15 + 15

= 30 square units.

Problem 13 :

Solution :

Area in the grid = area of triangle + 2 (area of parallelogram) + area of rectangle

base = 6 units, height = 3 units

base of parallelogram = 2 units and height = 1 unit

length of rectangle = 6 units and width = 2 units

= (1/2) x 6 x 3 + 2 x 2 x 1 + 6 x 2

= 3 x 3 + 4 + 12

= 9 + 4 + 12

= 25 square units.

Problem 14 :

Solution :

About trapezium :

Lengths of bases = 8 units and 4 units

About rectangle :

length = 4 units and width = 2 units

About traingle :

Base = 4 units and height = 2 units

Area in the grid = Area of trapezium + area of rectangle + area of triangle

= 8 x 4 + 4 x 2 + 4 x 2

= 32 + 8 + 8

= 48 square units.