- Perimeter and Area of Polygons
- Home
- Sides of polygons having the same perimeter
- Finding the missing length in a figure
- Perimeter of a piecewise rectangular figure
- Area of a rectangle involving fractions
- Distinguishing between the area and perimeter of a rectangle
- Areas of rectangles with the same perimeter
- Word problem involving the area of a square or a rectangle
- Finding the side length of a rectangle given its perimeter or area
- Area of a piecewise rectangular figure
- Area between two rectangles
- Finding the area of a right triangle on a grid
- Finding the area of a right triangle or its corresponding rectangle
- Area of a triangle
- Finding the area of a trapezoid on a grid by using triangles and rectangles
- Area involving rectangles and triangles
- Area of a parallelogram
- Area of a trapezoid
- Finding the perimeter or area of a rectangle in the coordinate plane

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# Sides of polygons having the same perimeter

In this lesson, we solve certain type of problems where we find side length of a polygon which has same perimeter as the given polygon.

Consider for an example: A wire is first bent in the shape of a rectangle of length 13 cm and 5 cm. Then this wire is unbent and reshaped into a square. We are now required to find the side length of this square.

It is clear that the length of the wire is fixed. The perimeter of the rectangle is the perimeter of the square. So we first find the perimeter of given rectangle using the formula 2(l + w). Since the rectangle is reshaped into a square, the perimeter of square is same as the perimeter of the rectangle.

Since all sides of a square are of equal length,

Side length of the square = $\frac{Square\:perimeter}{4}$ = $\frac{2(l + w)}{4}$

If the rectangle were reshaped into an equilateral triangle then the perimeter of the triangle would be same as the perimeter of the rectangle.

Since all sides of an equilateral triangle are of same length,

the side length of the equilateral triangle = $\frac{2(l + w)}{3}$

A wire is first bent into the shape of a rectangle with width 7 cm and 13 cm length. Then the wire is unbent and reshaped into a square. What is the length of a side of the square?

### Solution

**Step 1:**

Perimeter of rectangle = 2(7 + 13) = 40 cm

**Step 2:**

Perimeter of square = 40 cm

Side length of the square = $\frac{40}{4}$ = 10 cm

A wire is first bent into the shape of a rectangle with width 12 cm and 18 cm length. Then the wire is unbent and reshaped into a triangle. What is the length of a side of the triangle, if all its sides are equal?

### Solution

**Step 1:**

Perimeter of rectangle = 2(12 + 18) = 60 cm

**Step 2:**

Perimeter of equilateral triangle = 60 cm

Side length of the equilateral triangle = $\frac{60}{3}$ = 20 cm