## 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

= 1 cm + 0.6 cm

= 1.6 cm

Perimeter contributed by top rectangle

= 0.6 + 2.4 + 1.6

= 4.6 cm

= 0.6 + 2.4 + 1.6

= 4.6 cm

Perimeter contributed by bottom rectangle

= 0.6 + 2.4 + 1.6

= 4.6 cm

= 0.6 + 2.4 + 1.6

= 4.6 cm

Perimeter contributed by left quadrant

=

× ~~2~~

= 1.57 cm

=

1 |

_{2}4 |

^{1}× 3.14 × 1= 1.57 cm

Perimeter contributed by right quadrant

=

× ~~2~~

= 1.57 cm

=

1 |

_{2}4 |

^{1}× 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

=

= 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**#### 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

= 2 + 2

= 4 cm

Perimeter contributed by 1 quadrant

=

× ~~2~~~~2~~

= 1.57 cm

=

1 |

_{1}4 |

^{1}× 3.14 ×^{1}= 1.57 cm

Perimeter contributed by rectangle

= 0.2 + 2 + 0.2 + 2

= 4.4cm

= 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

=

= 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**#### 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

=

×

× ~~7~~

= 77 cm

=

1 |

_{1}2 |

_{11}22 |

_{1}7 |

^{1}× 7= 77 cm

^{2}
Area of medium semicircle

=

× 3.14 × 5 × 5

= 39.25 cm

=

1 |

2 |

= 39.25 cm

^{2}
Area of small semicircle

=

× 3.14 × 3 × 3

= 14.13 cm

=

1 |

2 |

= 14.13 cm

^{2}
Area of rectangle

= 10 × 2

= 20 cm

= 10 × 2

= 20 cm

^{2}
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

=

= Area of big semicircle

+ Area of rectangle

+ Area of medium semicircle

- Area of small semicircle

= 77 + 20 + 39.25 − 14.13

=

**122.12 cm**^{2}#### 4. Find the area of the shaded heart formed by 2 semicircles and a square.

Radius of semicircle

= 12 cm ÷ 2

= 6 cm

= 12 cm ÷ 2

= 6 cm

Area of two semicircles

= Area of 1 circle

= 3.14 × 6 × 6

= 113.04 cm

= Area of 1 circle

= 3.14 × 6 × 6

= 113.04 cm

^{2}
Area of square

= 12 × 12

= 144 cm

= 12 × 12

= 144 cm

^{2}
Area of shaded heart

= Area of 2 semicircles

+ Area of square

= 113.04 + 144

=

= Area of 2 semicircles

+ Area of square

= 113.04 + 144

=

**257.04 cm**^{2}#### 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

= 8 cm - 4 cm

= 4 cm

Area of 1 three-quarter circle

=

× 3.14 × ~~4~~

= 37.68 cm

=

3 |

_{1}4 |

^{1}× 4= 37.68 cm

^{2}
Height of right isosceles triangle

= Base of right isosceles triangle

= 4 + 10 cm = 14 cm

= Base of right isosceles triangle

= 4 + 10 cm = 14 cm

Area of big isosceles right triangle

=

× ~~14~~

= 98 cm

=

1 |

_{1}2 |

^{7}× 14= 98 cm

^{2}
Area of small isosceles right triangle

=

× ~~8~~

= 32 cm

=

1 |

_{1}2 |

^{7}× 8= 32 cm

^{2}
Area of square

= 8 × 8

= 64 cm

= 8 × 8

= 64 cm

^{2}**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 cm**

^{2}#### 6. Find the area and perimeter of the shaded figure below.

Diameter of semicircle

= 2.8 + 1.4 + 2.8

= 7 cm

= 2.8 + 1.4 + 2.8

= 7 cm

**PERIMETER**

Perimeter contributed by 1 semicircle

=

×

× ~~7~~

= 11 cm

=

1 |

_{1}2 |

_{11}22 |

_{1}7 |

^{1}= 11 cm

Perimeter contributed by 1 quadrant

=

× ~~2~~

× ~~2.8~~

= 4.4 cm

=

1 |

_{1}4 |

^{1}×_{11}22 |

_{1}7 |

^{0.4}= 4.4 cm

Perimeter contributed by rectangle

= 3.5 + 3.5 cm

= 7 cm

= 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

= 7 cm ÷ 2

= 3.5 cm

**AREA**

Area of 1 semicircle

=

×

× ~~3.5~~

= 19.25 cm

=

1 |

_{1}2 |

_{11}22 |

_{1}7 |

^{0.5}× 3.5= 19.25 cm

^{2}
Area of 1 square

= 2.8 × 2.8

= 7.84 cm

= 2.8 × 2.8

= 7.84 cm

^{2}
Area of 1 quadrant

=

×

× ~~2.8~~~~2.8~~

= 6.16 cm

=

1 |

_{1}4 |

22 |

_{1}7 |

^{0.7}×^{0.4}= 6.16 cm

^{2}
Length of rectangle

= 3.5 + 2.8 + 2.8

= 9.1 cm

= 3.5 + 2.8 + 2.8

= 9.1 cm

Area of rectangle

= 9.1 × 1.4

= 12.74 cm

= 9.1 × 1.4

= 12.74 cm

^{2}**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 cm**

^{2}