Let's break the problem into smaller parts in order to calculate the perimeter.

The diagram shows a ramp with different sections, including:

• Two straight sections of 2 meters each on the sides.
• Two curved sections forming half-circles with a radius of 2 meters.
• A triangular section at the bottom with sides $x$ and 2 meters at the base.

1. Calculate the value of $x$ (6.1):

We are told to use Pythagoras' theorem for the bottom triangular section.

• The base of the triangle is 2 meters.
• The height of the triangle is 2 meters.

Using the Pythagorean theorem: $x = \sqrt{2^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \approx 2.83 \, \text{m}.$

2. Calculate the perimeter (6.2):

Now, we calculate the perimeter by adding the lengths of all the segments:

1. Two straight vertical sides: Each side is 2 meters, so this contributes $2 \times 2 = 4 \, \text{m}$.
2. Two curved sections (semi-circles):
   • The total length of a full circle with radius 2 meters is: $\text{Circumference of full circle} = 2 \pi r = 2 \times 3.14 \times 2 = 12.56 \, \text{m}.$
   • Since the curved section is made of two half-circles, their total length is: $\text{Length of curved sections} = 12.56 \, \text{m}.$
3. Bottom triangle:
   • Two sides of the triangle are $x = 2.83$ meters, and 2 meters.
   • So, the total contribution from the triangle is: $\text{Length of triangle sides} = 2.83 + 2 = 4.83 \, \text{m}.$
4. Horizontal section (middle):
   • The middle horizontal section is 4 meters.

Total perimeter:

Adding all the components together: $\text{Perimeter} = 4 \, (\text{vertical sides}) + 12.56 \, (\text{curved sections}) + 4.83 \, (\text{triangle}) + 4 \, (\text{horizontal}) = 25.39 \, \text{m}.$

Thus, the total perimeter is approximately 25.39 meters.

Would you like more details or have any questions?

5 Follow-up questions:

1. What is the formula for the perimeter of a circle and how is it used here?
2. How would the perimeter change if the radius of the circular sections was doubled?
3. How does Pythagoras' theorem apply to the triangular part of the shape?
4. What is the effect of changing the horizontal section's length on the perimeter?
5. Could the same shape have a different perimeter if the ramp had different proportions?

Tip:

Always round your intermediate results carefully when performing multi-step calculations, as rounding errors can accumulate.