Two figures can have the same area but different perimeters. Is the given statement true or false?

Solution:

Given, two figures can have the same area but different perimeters.

We have to determine if the given statement is true or false.

Area is the amount of space occupied by a two-dimensional figure.

Perimeter is the total length of the boundary of any closed shape.

Let us consider two parallelograms.

The corresponding height and side of two parallelograms can be different.

Parallelogram 1:

(i) side 1 = 6 cm; side 2 = 4 cm; corresponding height with side 1 = 2 cm

Area of parallelogram = base × corresponding height

= 6 × 2

= 12 cm²

Perimeter = 2(a + b)

= 2(6 + 4)

= 2(10)

= 20 cm

Parallelogram 2:

(ii) side 1 = 4 cm; side 2 = 5 cm; corresponding height with side 1 = 3 cm

Area of parallelogram = base × corresponding height

= 4 × 3

= 12 cm²

Perimeter = 2(a + b)

= 2(4 + 3)

= 2(7)

= 14 cm

From the above examples, we observe that the perimeters are different but the areas are equal.

Therefore, the given statement is true.

✦ Try This: An increase in area of a figure always decreases the perimeter of the figure. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11

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NCERT Exemplar Class 7 Maths Chapter 9 Problem 71

Two figures can have the same area but different perimeters. Is the given statement true or false?

Summary:

The given statement, “Two figures can have the same area but different perimeters” is true.

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