Area and Perimeter of Composite Figures

1. The figure below is made of two identical rectangles and two identical quadrants. Find the perimeter of the shaded part.

Breadth of rectangle
= 1 cm + 0.6 cm
= 1.6 cm

Perimeter contributed by top rectangle
= 0.6 + 2.4 + 1.6
= 4.6 cm

Perimeter contributed by bottom rectangle
= 0.6 + 2.4 + 1.6
= 4.6 cm

Perimeter contributed by left quadrant
=

1

₂4

× 2¹× 3.14 × 1
= 1.57 cm

Perimeter contributed by right quadrant
=

1

₂4

× 2¹× 3.14 × 1
= 1.57 cm

Perimeter of shaded part
= Perimeter contributed by top rectangle
+ Perimeter contributed by left quadrant
+ Perimeter contributed by bottom rectangle
+ Perimeter contributed by right quadrant

= 4.6 + 1.57 + 4.6 + 1.57
= 12.34 cm

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2. The figure below shows two identical quadrants in two identical squares and a rectangle joining them to form a butterfly. Find the perimeter of the shaded butterfly.

Perimeter contributed by 1 square
= 2 + 2
= 4 cm

Perimeter contributed by 1 quadrant
=

1

₁4

× 2¹× 3.14 × 2¹
= 1.57 cm

Perimeter contributed by rectangle
= 0.2 + 2 + 0.2 + 2
= 4.4cm

Perimeter of shaded butterfly
= 2 × Perimeter contributed by 1 square
+ 2 × Perimeter contributed by 1 quadrant
+ Perimeter contributed by rectangle

= (2 × 4) + (2 × 3.14) + 4.4
= 8 + 6.28 + 4.4
= 18.68 cm

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3. Maddie joined 3 semicircles and a rectangle to form the shape of an umbrella. Find the area of the shaded umbrella.

Area of big semicircle
=

1

₁2

×

₁₁22

₁7

× 7¹× 7
= 77 cm²

Area of medium semicircle
=

1

2

× 3.14 × 5 × 5
= 39.25 cm²

Area of small semicircle
=

1

2

× 3.14 × 3 × 3
= 14.13 cm²

Area of rectangle
= 10 × 2
= 20 cm²

Area of shaded umbrella
= Area of big semicircle
+ Area of rectangle
+ Area of medium semicircle
- Area of small semicircle

= 77 + 20 + 39.25 − 14.13
= 122.12 cm²

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4. Find the area of the shaded heart formed by 2 semicircles and a square.

Radius of semicircle
= 12 cm ÷ 2
= 6 cm

Area of two semicircles
= Area of 1 circle
= 3.14 × 6 × 6
= 113.04 cm²

Area of square
= 12 × 12
= 144 cm²

Area of shaded heart
= Area of 2 semicircles
+ Area of square

= 113.04 + 144
= 257.04 cm²

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5. Find the area of the figure below formed by 2 identical three-quarter circles, 2 isosceles right-angled triangles and a square.

Radius of circle
= 8 cm - 4 cm
= 4 cm

Area of 1 three-quarter circle
=

3

₁4

× 3.14 × 4¹× 4
= 37.68 cm²

Height of right isosceles triangle
= Base of right isosceles triangle
= 4 + 10 cm = 14 cm

Area of big isosceles right triangle
=

1

₁2

× 14⁷× 14
= 98 cm²

Area of small isosceles right triangle
=

1

₁2

× 8⁷× 8
= 32 cm²

Area of square
= 8 × 8
= 64 cm²

Area of shaded figure
= 2 × Area of 1 three-quarter circle
+ Area of big isosceles triangle
+ Area of small isosceles triangle
+ Area of square

= (2 × 37.68) + 98 + 32 + 64
= 75.36 + 98 + 32 + 64
= 269.36 cm²

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6. Find the area and perimeter of the shaded figure below.

Diameter of semicircle
= 2.8 + 1.4 + 2.8
= 7 cm

PERIMETER

Perimeter contributed by 1 semicircle
=

1

₁2

×

₁₁22

₁7

× 7¹
= 11 cm

Perimeter contributed by 1 quadrant
=

1

₁4

× 2¹ ×

₁₁22

₁7

× ~~2.8~~^0.4
= 4.4 cm

Perimeter contributed by rectangle
= 3.5 + 3.5 cm
= 7 cm

Perimeter of shaded figure
= 2 × Perimeter contributed by 1 semicircle
+ 4 × Perimeter contributed by 1 quadrant
+ Perimeter contributed by rectangle

= (2 × 11) + (4 × 4.4) + 7
= 22 + 17.6 + 7
= 46.6 cm

Radius of semicircle
= 7 cm ÷ 2
= 3.5 cm

AREA

Area of 1 semicircle
=

1

₁2

×

₁₁22

₁7

× ~~3.5~~^0.5 × 3.5
= 19.25 cm²

Area of 1 square
= 2.8 × 2.8
= 7.84 cm²

Area of 1 quadrant
=

1

₁4

×

22

₁7

× ~~2.8~~^0.7 × ~~2.8~~^0.4
= 6.16 cm²

Length of rectangle
= 3.5 + 2.8 + 2.8
= 9.1 cm

Area of rectangle
= 9.1 × 1.4
= 12.74 cm²

Area of shaded figure
= 2 × Area contributed by 1 semicircle
+ 4 × (Area of 1 square − Area of 1 quadrant)
+ Area of rectangle

= (2 × 19.25) + (4 × (7.84 − 6.16))+ 12.74
= 38.5 + 6.72 + 12.74
= 57.96 cm²

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