Question

Could the area of a square and the area of a circle both be 100 cm2? Explain.

Answer 1

No, the area of a square and the area of a circle cannot both be 100 cm².

Step-by-step explanation:

The area of a square is found by multiplying the length of one of its sides by itself. So if the area of a square is 100 cm2, the side length would be 10 cm since 10 x 10 = 100. On the other hand, the area of a circle is found by multiplying the square of its radius by pi (approximately 3.14). To have an area of 100 cm2, the radius would need to be approximately 5.64 cm, which is not equal to the side length of the square. Therefore, the area of a square and the area of a circle cannot both be 100 cm2.

Answer 2

no

Step-by-step explanation:

since a square is equilateral, each side must be 10 to produce an area of 100 sq cm

the formula for the area of a circle is: A = πr²

if we substitute 100 for 'A' we get:

100 = πr²

100/π = r²

31.84 = r²

since 31.84 is not a perfect square then the radius and/or diameter is not a whole number