# Area and Perimeter of Composite Figures

### Problem 1

The figure below is made of two identical rectangles and two identical quadrants. Find the perimeter of the shaded part. = 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 = 142 × 21 × 3.14 × 1 = 1.57 cm
 Perimeter contributed by right quadrant = 142 × 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

### Problem 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 = 1421 × 21 × 3.14 × 21 = 3.14 cm
 Perimeter contributed by rectangle = 0.2 + 2 + 0.2 + 2 = 4.4 cm

 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

### Problem 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  =
 121 × 221171 × 71 × 7
=  77 cm2
= 2 cm + 3 cm = 5 cm

 Area of medium semicircle = 12 × 3.14 × 5 × 5 = 39.25 cm2

 Area of small semicircle = 12 × 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

### Problem 4

Find the area of the shaded heart formed by 2 semicircles and a square. = 12 m ÷ 2
= 6 m
 Area of 2 semicircles = Area of 1 circle = 3.14 × 6 × 6 = 113.04 m2

 Area of square = 12 × 12 = 144 m2

 Area of shaded heart = Area of 2 semicircles + Area of square = 113.04 + 144 = 257.04 m2

### Problem 5

Find the area of the figure below formed by 2 identical three-quarter circles, 2 isosceles right-angled triangles and a square. = 8 cm − 4 cm
= 4 cm

 Area of 1 three-quarter circle = 341 × 3.14 × 41 × 4 = 37.68 cm2

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

 Area of big isosceles right triangle = 121 × 147 × 14 = 98 cm2

 Area of small isosceles right triangle = 121 × 84 × 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

### Problem 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 = 121 × 221171 × 71 = 11 cm

 Perimeter contributed by 1 quadrant = 1421 × 21 × 221171 × 2.80.4 = 4.4 cm

 Perimeter contributed by rectangle = 3.5 + 3.5 = 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

= 7 cm ÷ 2
= 3.5 cm

AREA

 Area of 1 semicircle = 121 × 221171 × 3.50.5 × 3.5 = 19.25 cm2

 Area of 1 square = 2.8 × 2.8 = 7.84 cm2

 Area of 1 quadrant = 141 × 2271 × 2.80.7 × 2.80.4 = 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 shape = 2 × Area of 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