Question

a star is inside a square of side length 8cm the star covers 40% area of the square The same star is placed inside a rectangle with width 8cm the length of the rectangle is 60% longer than the width calculate the percentage of the rectangle that the star covers

Answer 1

Explanation:

The area of the square is:

A = side^2 = 8^2 = 64 cm^2

Since the star covers 40% of the area of the square, its area is:

a_star = 0.4 * 64 = 25.6 cm^2

Let the width of the rectangle be 8 cm. Then, the length of the rectangle is:

l = 8 + 0.6*8 = 12.8 cm

The area of the rectangle is:

A_rect = wl = 812.8 = 102.4 cm^2

To calculate the area of the star inside the rectangle, we need to know the dimensions of the rectangle that are covered by the star. Since the star is inside a square of side 8 cm, its maximum width and height are both 8 cm. Therefore, the maximum area of the star inside the rectangle is:

a_star_max = 8*8 = 64 cm^2

However, this area is larger than the area of the star itself, which is 25.6 cm^2. Therefore, the area of the star inside the rectangle is 25.6 cm^2.

The percentage of the rectangle that the star covers is:

% coverage = (area of star inside rectangle / area of rectangle) * 100

= (25.6 / 102.4) * 100

= 25%

Therefore, the star covers 25% of the rectangle.