Thread: rectangle and square

I need help in the below problem

The figure is made up of a square and a rectangle. The ratio of the area of the square to the area of the rectangle is 2 : 5. I/4 of the square is shaded.
What fraction of the figure is unshaded?

Originally Posted by kingman

I need help in the below problem

The figure is made up of a square and a rectangle. The ratio of the area of the square to the area of the rectangle is 2 : 5. I/4 of the square is shaded.
What fraction of the figure is unshaded?

Let the areas of the square and the rectangle be 2 and 5 respectively.

Area of the shaded area = 1/4 * 2 = 0.5

Total area = 2 + 5 - 0.5 = 6.5

Area of the unshaded area = 6.5 - 0.5 = 6

Fraction unshaded = 6 / 6.5 = 12 / 13

Hello, kingman!

Another approach . . .

The figure is made up of a square and a rectangle.
The ratio of the area of the square to the area of the rectangle is 2:5.
I/4 of the square is shaded.
What fraction of the figure is unshaded?

Code:

      * - - - - - - - *
      |               |
      |               |
      |     C     * - + - *
      |           |:::|   |
      |           |:A:|   |
      * - - - - - + - *   |
                  |       |
                  |   B   |
                  * - - - *

Let = area of the square.
Let = area of the rectangle.

We have: .

We have: .

Then: .


The unshaded area is: .

The total area is: .


Therefore: .

Originally Posted by Soroban

Hello, kingman!

Another approach . . .

Code:

    * - - - - - - - *
    |               |
    |               |
    |     C     * - + - *
    |           |:::|   |
    |           |:A:|   |
    * - - - - - + - *   |
                |       |
                |   B   |
                * - - - *

Let = area of the square.
Let = area of the rectangle.

We have: .

We have: .

Then: .


The unshaded area is: .

The total area is: .


Therefore: .

I wonder why all the numbers and text displayed are blurred; so cannot figure out what is wriiten on the solution page.
thanks