To solve the problem presented in the image, let's break down each part of the question and solve it step by step. The problem involves a rectangular metal sheet with a semicircular part removed. The sheet dimensions are given as 20 cm by 14 cm, and the semicircular part has been cut from one end. Here are the steps we need to follow:

Part (i): Find the value of $h$

We assume $h$ represents the height from the center of the semicircle's diameter to the farthest point on the rectangle. Given the radius of the semicircle:

• The semicircle has a diameter of 14 cm (equal to the breadth of the rectangle), so the radius $r$ is: $r = \frac{14}{2} = 7 \, \text{cm}$

The value of $h$ is equal to the radius $r$ of the semicircle. Thus: $h = 7 \, \text{cm}$

Part (ii): Calculate the area of the semicircular part removed

The area $A$ of a semicircle is given by: $A = \frac{1}{2} \pi r^2$ Substitute $r = 7 \, \text{cm}$: $A = \frac{1}{2} \pi (7)^2 = \frac{1}{2} \pi \times 49 = 24.5 \pi \approx 76.96 \, \text{cm}^2$

So, the area of the semicircular part removed is approximately $76.96 \, \text{cm}^2$.

Part (iii): Find the area of the shaded region

To find the area of the shaded region, we need to calculate the area of the original rectangular metal sheet and then subtract the area of the semicircular part that was removed.

1. Area of the rectangle: $\text{Area of rectangle} = \text{length} \times \text{breadth} = 20 \, \text{cm} \times 14 \, \text{cm} = 280 \, \text{cm}^2$

2. Subtract the area of the semicircle: [ \text{Shaded area} = \text{Area of rectangle} - \text{Area of semicircle} = 280 , \text{cm}^2 - 76.96 , \text{cm}^2