The image shows a figure consisting of a semicircle and a rectangle with a triangle cut out of it. We are tasked with finding the area of the figure, using $\pi = 3.14$.

Given measurements:

• Length of the rectangle: $30 \, \text{m}$
• Width of the rectangle: $12 \, \text{m}$
• The semicircle is on the left, with a diameter equal to the width of the rectangle: $12 \, \text{m}$
• The triangle is right-angled, with the base of $10 \, \text{m}$ and the height matching the width of the rectangle ($12 \, \text{m}$).

Steps to solve:

1. Area of the rectangle: $\text{Area of the rectangle} = \text{Length} \times \text{Width} = 30 \, \text{m} \times 12 \, \text{m} = 360 \, \text{m}^2$

2. Area of the semicircle: The diameter of the semicircle is $12 \, \text{m}$, so the radius is $6 \, \text{m}$. $\text{Area of the semicircle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.14 \times 6^2 = \frac{1}{2} \times 3.14 \times 36 = 56.52 \, \text{m}^2$

3. Area of the triangle: The triangle is right-angled with base $10 \, \text{m}$ and height $12 \, \text{m}$. $\text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \, \text{m} \times 12 \, \text{m} = 60 \, \text{m}^2$

4. Total area of the figure: $\text{Total area} = \text{Area of the rectangle} + \text{Area of the semicircle} - \text{Area of the triangle}$ $\text{Total area} = 360 \, \text{m}^2 + 56.52 \, \text{m}^2 - 60 \, \text{m}^2 = 356.52 \, \text{m}^2$

Final Answer:

The area of the figure is $356.52 \, \text{m}^2$.

Do you need further details or have any questions?

Here are 5 related questions to expand on this:

1. How do we calculate the circumference of a semicircle?
2. What is the perimeter of the entire figure if we include the triangle's cut-out?
3. How would the calculation change if the triangle were not right-angled?
4. What formula is used to find the area of a full circle?
5. How can we derive the formula for the area of a right-angled triangle?

Tip: In geometry, breaking complex shapes into simpler ones like rectangles, triangles, and circles often simplifies area calculations.