Question

Calculate each shaded area. All measurements are in cm

Answer 1

Answer:

area of shaded region for pic 1= 27.43cm²

area of shaded region for pic 2=115.5cm²

Step-by-step explanation:

Answer 2

(1)Area of shaded region=$27.43m^2$

(2)Area of shaded region=$57.75cm^2$

Step-by-step explanation:

In first figure

Diameter of each circle=d=8 m

Radius of circle=$\frac{d}{2}=\frac{8}{2}=4m$

Length of rectangle=8+8=16 m

Breadth of rectangle=8 m

Area of circle=$\pi r^2$

Where $\pi=\frac{22}{7}$

r=Radius of circle

Using the formula

Area of 1 circle=$\frac{22}{7}\times (4)^2$ square meter

Area of two circles=$2\times \frac{22}{7}\times (4)^2=100.57 m^2$

Area of rectangle=$length\times breadth$

Using the formula

Area of rectangle=$16\times 8=128m^2$

Area of shaded region= Area of rectangle-Area of two circles

Area of shaded region=$128-100.57=27.43m^2$

Area of shaded region=$27.43m^2$

In second figure

Diameter of big semi circle,d=14 cm

Radius of big semi =$\frac{14}{2}=7cm$

Area of semi -circle=$\frac{1}{2}\pi r^2$

Area of big semi circle=$\frac{1}{2}\times \frac{22}{7}\times (7)^2=77 cm^2$

Diameter of small circle=Radius of big circle=7 cm

Radius of small circle=$\frac{7}{2} cm$

Area of small circle=$\frac{1}{2}\times \frac{22}{7}\times (\frac{7}{2})^2=19.25 cm^2$

Area of shaded region=Area of big semi-circle-area of small semi-circle

Area of shaded region=$77-19.25=57.75cm^2$

Area of shaded region=$57.75cm^2$

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