Question

compare the areas of a square 12cm on each side and a rectangle 10 cm by 9 cm which figure has the greater area and by how much ?

Answer 1

Given:-

• Side of square = 12 cm
• Length of rectangle = 10 cm
• Breadth of rectangle = 9 cm

To Find:-

• Which figure has the greater area and by how much.

Solution:

Let us first find the area of square.

We know,

• Area of square = (side)²

Hence,

Area of square = (12)²

Area of square = 144 cm²

Now,

Let us find the area of rectangle

We know,

• Area of rectangle = Length × Breadth

Hence,

Area of rectangle = 10 × 9

Area of rectangle = 90 cm²

Now,

We got:-

• Area of square = 144 cm²
• Area of rectangle = 90 cm²

Here we can clearly see:-

Area of square > Area of rectangle.

∴ Square has greater area.

Now,

Let us calculate by how much is the area od square greater than the area of rectangle.

= Area of square - Area of rectangle

= 144 - 90

= 54 cm²

∴ Area of square is greater than the area of rectangle by 54 cm².

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Formulas used:-

• Area of square = (side)² sq.units
• Area of rectangle = (Length × Breadth) sq.units.

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Answer 2

Given:

A square with

• Side = 12 cm

A rectangle with

• Length = 10 cm
• Breadth = 9 cm

What To Find:

We have to find

• The area of square and rectangle
• Compare which one has greater area by how much

Solution:

• Finding the area of square

Using the formula,

⇒ Area = side × side

Substitute the values,

⇒ Area = 12 cm × 12 cm

Multiply the sides,

⇒ Area = 144 cm²

• Finding the area of rectangle

Using the formula,

⇒ Area = length × breadth

Substitute the values,

⇒ Area = 10 cm × 9 cm

Multiply the sides,

⇒ Area = 90 cm²

• Finding the greater area and by how much

1. Finding the greater area

Area of square = 144 cm²

Area of rectangle = 90 cm²

As we can see that

144 cm² > 90 cm²

Area of square > Area of rectangle

2. Finding by how much

Area of square - Area of rectangle = Greater area by how much

Substitute the values,

⇒ 144 cm² - 90 cm² = Greater area by how much

Subtract the areas,

⇒54 cm² = Greater area by how much

∴ Therefore, the area of square is greater by 54 cm².