Question

A square and a circle both have a perimeter of 176 cm .which one has more area and how much ?

Answer 1

Answer:

area of circle is more that area of square by 528 cm²

Step-by-step explanation:

SQUARE:

we know,

perimeter of square = 4a

⇒ 4a = 176

⇒ a = 44 cm

we know,

area of square = a²

= (44)²

area of square = 1936 cm²

CIRCLE:

we know,

perimeter of circle = 2πr

2πr = 176

r = 7(176)/2(22)

r = 28 cm

we know,

area of circle = πr²

= 22(28)²/7

area of circle = 2464 cm²

therefore area of circle is more that area of square by 528 cm²

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Answer 2

Answer:

• Area of circle is more by 528 cm².

Step-by-step explanation:

Given:

• Square and circle both have same perimeter = 176 cm

To Find:

• Which one has more area and how much?

Now, we know that,

$\longrightarrow \bf Perimeter\;of\;square=4\times side\\ \\ \\ \longrightarrow \sf 176 = 4\times side \\ \\ \\ \longrightarrow \sf Side\;of\;square=\dfrac{176}{4}\\ \\ \\ \longrightarrow {\boxed{\bf Side\;of\;square=44\;cm}}\\ \\ \rule{200}{2}\\ \\ \bf Now, Area\;of\;square=side\times side \\ \\ \\ \longrightarrow \sf Area\;of\;square=44\times 44\\ \\ \\ \longrightarrow {\boxed {\bf Area\;of\;square=1936\;cm^{2}}}$

$\rule{200}{2}$

$\longrightarrow \bf Perimeter\;of\;circle=2\pi r\\ \\ \\ \longrightarrow \sf 176=2\times \dfrac{22}{7}\times r\\ \\ \\ \longrightarrow {\boxed{\bf Radius\;of\;circle = 28\;cm}}\\ \\ \rule{200}{2}\\ \\ \longrightarrow \bf Now,\;Area\;of\;circle=\pi r^{2}\\ \\ \\ \longrightarrow \sf Area\;of\;circle=\dfrac{22}{7}\times 28\times 28\\ \\ \\ \longrightarrow \sf Area\;of\;circle= 22\times 4\times 28\\ \\ \\ \longrightarrow {\boxed{\bf Area\;of\;circle = 2464\;cm^{2}}}$

$\rule{200}{2}$

Which one has more area and how much?

$\therefore {\boxed{\bf Area\;of\;circle\;is\;more\; by\;2464-1936=528\;cm^{2}}}$

$\rule{200}{2}$

Hence, Area of circle is more by 528 cm².

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