Question

calculate the length of boundary and the area of shaded region in the following diagrams. all measurements are in centimeters. 1) unshaded part is a semicircle.

Answer 1

area of the shaded region= area of rectangle- area of semicircle
ans = l*b - 1/2*pi r^2
7*10 - 1/2*22/7* 7/2*7/2
70 - 19.25
= 50.75cm^2

Answer 2

Length of boundary is 38 (cm) and area of shaded region is $\mathbf{50.75(cm^{2})}$

Step-by-step explanation:

1. Length of rectangle (L)= 10(cm)

  Breadth of rectangle(B) = Diameter of semicircle(D) =7(cm)

  Radius of semicircle $\mathbf{(R)=\frac{D}{2}=\frac{7}{2}(cm)}$

2. Circumference of semicircle $\mathbf{(P_{c})=\pi R=\frac{22}{7}\times \frac{7}{2}=11 (cm)}$

3. Area of semicircle $\mathbf{(A_{c})=\frac{\pi R^{2}}{2}=\frac{1}{2}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}=19.25 (cm^{2})}$

   Area of Rectangle $\mathbf{(A_{R})=L\times B= 10\times 7=70 (cm^{2})}$

4. Length of boundary $\mathbf{=L+B+L+P_{c}}$

   Length of boundary $\mathbf{=10+7+10+11=38(cm)}$

5. Area of shaded region =Area of rectangle - Area of semi circle

   Area of shaded region =70-19.25=$\mathbf{50.75(cm^{2})}$