Find The Perimeter Of The Figure Below.(Take $\pi = \frac{22}{7}$, $\beta = 3.5$) Age $= 75$

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Introduction

In mathematics, finding the perimeter of a complex figure involves breaking down the figure into its individual components, such as lines, arcs, and curves, and then calculating the total distance around the figure. In this article, we will discuss how to find the perimeter of a complex figure using the given values of π=227\pi = \frac{22}{7} and β=3.5\beta = 3.5.

Understanding the Figure

The figure below consists of a rectangle with a semicircle at the top and a triangle at the bottom. The rectangle has a length of 10 units and a width of 5 units. The semicircle has a radius of 4 units, and the triangle has a base of 6 units and a height of 3 units.

Figure Components

  • Rectangle: 10 units (length) x 5 units (width)
  • Semicircle: 4 units (radius)
  • Triangle: 6 units (base) x 3 units (height)

Calculating the Perimeter of the Rectangle

The perimeter of a rectangle is calculated by adding the lengths of all its sides. Since the rectangle has two pairs of equal sides, we can calculate the perimeter as follows:

Perimeter of rectangle = 2(length + width) = 2(10 + 5) = 2 x 15 = 30 units

Calculating the Perimeter of the Semicircle

The perimeter of a semicircle is calculated by adding the length of the base and the curved part. Since the semicircle has a radius of 4 units, we can calculate the perimeter as follows:

Perimeter of semicircle = πr + 2r = (22/7) x 4 + 2 x 4 = (22/7) x 4 + 8 = 25.71 + 8 = 33.71 units

Calculating the Perimeter of the Triangle

The perimeter of a triangle is calculated by adding the lengths of all its sides. Since the triangle has a base of 6 units and a height of 3 units, we can calculate the perimeter as follows:

Perimeter of triangle = a + b + c = 6 + 3 + 5 (using the Pythagorean theorem) = 14 units

Calculating the Total Perimeter

To find the total perimeter of the complex figure, we need to add the perimeters of the rectangle, semicircle, and triangle.

Total perimeter = Perimeter of rectangle + Perimeter of semicircle + Perimeter of triangle = 30 + 33.71 + 14 = 77.71 units

Conclusion

In this article, we discussed how to find the perimeter of a complex figure using the given values of π=227\pi = \frac{22}{7} and β=3.5\beta = 3.5. We broke down the figure into its individual components, calculated the perimeter of each component, and then added them together to find the total perimeter. The total perimeter of the complex figure is 77.71 units.

Additional Tips and Tricks

  • When dealing with complex figures, it's essential to break them down into their individual components to make calculations easier.
  • Use the given values of Ï€\pi and β\beta to calculate the perimeters of the semicircle and triangle.
  • When adding the perimeters of the components, make sure to include the curved part of the semicircle.

Frequently Asked Questions

  • Q: What is the perimeter of a rectangle? A: The perimeter of a rectangle is calculated by adding the lengths of all its sides.
  • Q: What is the perimeter of a semicircle? A: The perimeter of a semicircle is calculated by adding the length of the base and the curved part.
  • Q: What is the perimeter of a triangle? A: The perimeter of a triangle is calculated by adding the lengths of all its sides.

References

Introduction

In our previous article, we discussed how to find the perimeter of a complex figure using the given values of π=227\pi = \frac{22}{7} and β=3.5\beta = 3.5. In this article, we will answer some frequently asked questions related to the perimeter of a complex figure.

Q&A

Q: What is the perimeter of a rectangle?

A: The perimeter of a rectangle is calculated by adding the lengths of all its sides. Since a rectangle has two pairs of equal sides, we can calculate the perimeter as follows:

Perimeter of rectangle = 2(length + width) = 2(10 + 5) = 2 x 15 = 30 units

Q: What is the perimeter of a semicircle?

A: The perimeter of a semicircle is calculated by adding the length of the base and the curved part. Since the semicircle has a radius of 4 units, we can calculate the perimeter as follows:

Perimeter of semicircle = πr + 2r = (22/7) x 4 + 2 x 4 = (22/7) x 4 + 8 = 25.71 + 8 = 33.71 units

Q: What is the perimeter of a triangle?

A: The perimeter of a triangle is calculated by adding the lengths of all its sides. Since the triangle has a base of 6 units and a height of 3 units, we can calculate the perimeter as follows:

Perimeter of triangle = a + b + c = 6 + 3 + 5 (using the Pythagorean theorem) = 14 units

Q: How do I calculate the total perimeter of a complex figure?

A: To find the total perimeter of a complex figure, you need to add the perimeters of all its components. In our previous article, we calculated the perimeters of the rectangle, semicircle, and triangle, and then added them together to find the total perimeter.

Total perimeter = Perimeter of rectangle + Perimeter of semicircle + Perimeter of triangle = 30 + 33.71 + 14 = 77.71 units

Q: What is the formula for the perimeter of a circle?

A: The formula for the perimeter of a circle is:

Perimeter of circle = 2Ï€r = 2 x (22/7) x 4 = 2 x 22/7 x 4 = 2 x 22 x 4/7 = 2 x 88/7 = 176/7 = 25.14 units

Q: What is the formula for the perimeter of an ellipse?

A: The formula for the perimeter of an ellipse is:

Perimeter of ellipse = π x (3(a + b) - √((3a + b)(a + 3b))) where a and b are the lengths of the semi-major and semi-minor axes, respectively.

Q: How do I calculate the perimeter of a polygon?

A: To calculate the perimeter of a polygon, you need to add the lengths of all its sides. Since a polygon has multiple sides, you can use the formula:

Perimeter of polygon = a + b + c + ... where a, b, c, ... are the lengths of the sides of the polygon.

Q: What is the perimeter of a complex figure with multiple components?

A: To find the perimeter of a complex figure with multiple components, you need to add the perimeters of all its components. In our previous article, we calculated the perimeters of the rectangle, semicircle, and triangle, and then added them together to find the total perimeter.

Conclusion

In this article, we answered some frequently asked questions related to the perimeter of a complex figure. We discussed how to calculate the perimeters of various shapes, including rectangles, semicircles, triangles, circles, ellipses, and polygons. We also provided formulas and examples to help you understand the concepts better.

Additional Tips and Tricks

  • When dealing with complex figures, it's essential to break them down into their individual components to make calculations easier.
  • Use the given values of Ï€\pi and β\beta to calculate the perimeters of the semicircle and triangle.
  • When adding the perimeters of the components, make sure to include the curved part of the semicircle.

Frequently Asked Questions

  • Q: What is the perimeter of a rectangle? A: The perimeter of a rectangle is calculated by adding the lengths of all its sides.
  • Q: What is the perimeter of a semicircle? A: The perimeter of a semicircle is calculated by adding the length of the base and the curved part.
  • Q: What is the perimeter of a triangle? A: The perimeter of a triangle is calculated by adding the lengths of all its sides.

References