Perimeter of Other Shapes

In geometry, it is important to understand shapes and their properties. An important way to learn about shapes is to find their perimeter. The perimeter is the total length of the boundary of a shape. In this lesson, we will find the perimeter of various other shapes beyond the usual rectangles and squares. Let's understand these concepts in depth with text examples and simple visual examples.

Understanding the perimeter

The perimeter of a shape is the total distance around the shape. To calculate the perimeter, we simply add up the lengths of all the sides. The perimeter helps us understand how much space a shape occupies along its boundary.

Perimeter of common shapes

Perimeter of a triangle

The perimeter of a triangle is the sum of the lengths of its three sides. Let's take a look at the formula:

    Perimeter of a triangle = Side 1 + Side 2 + Side 3

Example:

Consider a triangle whose sides are 3 cm, 4 cm and 5 cm. The perimeter will be calculated as follows:

    Perimeter = 3 cm + 4 cm + 5 cm = 12 cm

Perimeter of a parallelogram

A parallelogram is a four-sided shape in which opposite sides are equal. The perimeter is calculated by adding the lengths of two adjacent sides and multiplying by two:

    Perimeter of parallelogram = 2 × (base + side)

Example:

Let's find the perimeter of a parallelogram with a base of 6 cm and a side of 4 cm:

    Perimeter = 2 × (6 cm + 4 cm) = 2 × 10 cm = 20 cm

Perimeter of rhombus

A rhombus is a special type of parallelogram, with all sides equal. To calculate the perimeter of a rhombus, multiply the length of one side by four:

    Perimeter of rhombus = 4 × side

Example:

If the side of a rhombus is 5 cm, then the perimeter is:

    Perimeter = 4 × 5 cm = 20 cm

Perimeter of less common shapes

Circumference of a kite

A kite is a four-sided shape in which two pairs of adjacent sides are equal. One way to find the perimeter of a kite is to add up the lengths of all four sides:

    Perimeter of the kite = 2 × (side 1 + side 2)

Example:

For a kite with side measurements 3 cm and 4 cm, the perimeter is calculated as:

    Perimeter = 2 × (3 cm + 4 cm) = 2 × 7 cm = 14 cm

Perimeter of trapezium

A trapezoid (also called a trapezoid) is a four-sided shape with a pair of parallel sides. To find the perimeter of a trapezoid, simply add up the lengths of all its sides:

    Perimeter of trapezium = base 1 + base 2 + side 1 + side 2

Example:

Consider a trapezoid with base measurements of 8 cm and 5 cm, and side measurements of 4 cm and 3 cm:

    Perimeter = 8 cm + 5 cm + 4 cm + 3 cm = 20 cm

Perimeter of complex shapes

Mixed shapes

Compound shapes are made up of two or more basic shapes. To find the perimeter of a compound figure, identify and separate the individual shapes it contains, calculate their perimeters, and then add them accordingly. Below are some examples of working with compound shapes.

Perimeter of a figure with edges that follow known shapes

Example:

Let's calculate the perimeter of a figure that consists of a rectangle connected to a semicircle. The length of the rectangle = 6 cm and width = 4 cm, and the diameter of the semicircle is 4 cm:

    Perimeter of the rectangle = 2 × (6 cm + 4 cm) = 20 cm
    Circumference of full circle = π × diameter = 3.14 × 4 cm = 12.56 cm
    Perimeter of semicircle = 12.56 cm ÷ 2 = 6.28 cm
    Total perimeter = 20 cm + 6.28 cm = 26.28 cm

Custom size

For custom shapes, consider each individual section and see how they contribute to the overall boundary of the shape. Use the techniques described above to find the perimeter.

Application of perimeter

Understanding perimeter is useful in many real-world applications, such as planning a garden layout or determining the amount of material needed for boundary fencing.

In short, knowing how to calculate the perimeter is very helpful in understanding geometry better and solving practical problems. Remember to add all sides and use the properties of known shapes to calculate the perimeter efficiently.

By mastering the perimeter of various shapes, we build a strong foundation for more advanced geometric studies and real-world problem-solving.

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