Question

Two figures can have the same area but different perimeters.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Because the perimeter is the sum of all sides of closed shapes or polygons while the area is just bounded space insides.

 

Let's take example of parallelogram

 

Their corresponding height and sides may different.

 

Thus, perimeter cannot be equal, even though area is equal

 

Example:

 

parallelogram 1: Side 1 = 6, Side 2 = 3, Height with side 1 base = 2.5

 

So, Area = 6 × 2.5 = 15

 

And perimeter = 2 × 6 + 2 × 3 = 12 + 6 = 18

 

Let, parallelogram 2: Side 1 = 5, Side 2 = 3.5, Height with side 1 base = 3

 

So, Area = 5 × 3 = 15

 

And perimeter = 2 × 5 + 2 × 3.5 = 10 + 7 = 17