Question

Here are two squares A and B. The length of the side A is 50% of the length of the side square B. Express the area of the shaded region of square A as a percentage of the area of square B.

Please answer quickly!!

Answer 1

Answer: 12.5%

Explanation:

==>Given:

Square A side length = 50% Square B side length

Area of Square A that is shaded = ½ of the area of Square B

==>Required:

Area of shaded region of Square A as a % of Area of Square B

==>Solution:

Let "b" be the side length of Square B

Let "a" be the side length of Square A

Since we are told that the side length of Square A (a) = 50% of side length of Square B (b), thus we have,

a = ½b

==>Let's find the area of Square A and Square B:

Area of a square = s², where s = side length

Area of Square A = (½b)² = b²/4

Area of Square B = b²

==>Let's find the area of the shaded region of the Square A = ½ of area of Square A.

Thus,

Area of shaded region of Square A = ½*(b²/4) = b²/8

==>Let's express the area of the shaded portion of square A as a percentage of are of Square B:

Thus, Area of shaded portion of Square A ÷ Area of Square B × 100%

The area of the shaded region of Square A is 12.5% of the area of Square B.

Answer 2

12.5%

Explanation:

==>Given:

Square A side length = 50% Square B side length

Area of Square A that is shaded = ½ of the area of Square B

==>Required:

Area of shaded region of Square A as a % of Area of Square B

==>Solution:

Let "b" be the side length of Square B

Let "a" be the side length of Square A

Since we are told that the side length of Square A (a) = 50% of side length of Square B (b), thus we have,

a = ½b

==>Let's find the area of Square A and Square B:

Area of a square = s², where s = side length

Area of Square A = (½b)² = b²/4

Area of Square B = b²

==>Let's find the area of the shaded region of the Square A = ½ of area of Square A.

Thus,

Area of shaded region of Square A = ½*(b²/4) = b²/8

==>Let's express the area of the shaded portion of square A as a percentage of are of Square B:

Thus, Area of shaded portion of Square A ÷ Area of Square B × 100%

`= ((b^(2) )/(8) )/(b^(2) ) * 100`

`= (b^(2) )/(8) * (1)/(b^(2) ) * 100`

`= (b^(2)*1 )/(8*b^(2) ) * 100`

`= (b^(2) )/(8*b^(2) ) * 100`

`= (1)/(8) * 100 = 12.5`

The area of the shaded region of Square A is 12.5% of the area of Square B.