Same Perimeter Different Area

Perimeter is nothing but the path around the shape. And area is nothing but the space occupied by the 2 dimensional object. Here we are going to deal with the same perimeter and different area of the shape. Every shape is having different formulas for area. And for all shape if we want to find the perimeter we have to add the length of all sides. We will see some example problems for same perimeter and different area.

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Example Problems for same Perimeter and Different Area:

Example 1 for same perimeter and different area:



Find the area and perimeter of the following shapes and compare the area and perimeter.

Solution:

Shape 1:

The first shape is a rectangle. We know the area of the rectangle is l X w

Here length l = 3 cm and the width w = 4 cm

So the area of the rectangle = 3 X 4 = 12 cm2

Perimeter of the rectangle is = 2 (l + w) = 2 (3 + 4) = 2 X 7 =14 cm.

Shape 2:

The shape 2 is a triangle. To find the area of the triangle we have to use the following formula.

Area of the triangle = (`1 / 2` ) bh.

From the above b = 7 cm and h = 2 cm.

So the area =` (1 / 2) xx 7 xx 2 ` = 7 cm2

Perimeter of the triangle   = sum of all sides = 7 + 4 +3 = 14 cm.

From the above bath shape is having the same perimeter and different area.

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Example 2 for same Perimeter and Different Area:

Find the area and perimeter of the following shapes and compare the area and perimeter.



Solution:

Shape 1:

The first shape is a trapezoid. We know the area of the trapezoid is `(1/2) h (a + b)`

Here a and b are the base lengths. A = 6 cm. b = 4 cm and the height is 5 cm.

So the area of the rectangle = `(1/2) 5 (6 + 4) ` = 25 cm2

Perimeter of the rectangle is = sum of all sides = 6 + 5 + 4 + 3 = 18 cm.

Shape 2:

The second shape is a rectangle. We know the area of the rectangle is l X w

Here length l = 6 cm and the width w = 3 cm

So the area of the rectangle = 6 `xx` 3 = 18 cm2

Perimeter of the rectangle is = 2 (l + w) = 2 (6 + 3) = 2 X 9 =18 cm.

From the above bath shape is having the same perimeter and different area.

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