Thread: Ratios of Area in Rectangles

These two problems are giving me a lot of trouble. If any one could give me some help in the right direction I'd really appreciate it.

1 In rectangle ABCD, point E is on side AB so that AE = 10 and EB = 5. What fraction of the area of the rectangle is inside triangle AEC?

2 M and N are the midpoints of consecutive sides of a square ABCD with vertex A in between M and N. What is the ratio of the area of triangle AMN to the area of the complete square.

Thanks again.

Originally Posted by lyyy94

These two problems are giving me a lot of trouble. If any one could give me some help in the right direction I'd really appreciate it.

1 In rectangle ABCD, point E is on side AB so that AE = 10 and EB = 5. What fraction of the area of the rectangle is inside triangle AEC?

2 M and N are the midpoints of consecutive sides of a square ABCD with vertex A in between M and N. What is the ratio of the area of triangle AMN to the area of the complete square.

Thanks again.

1) Area of ABCD = AB*BC
Area of AEC = 1/2*AE*BC

Hello, lyyy94!

1. In rectangle , point is on side so that: .
What fraction of the area of the rectangle is inside triangle ?

Code:

      :      10       E   5   :
    A o - - - - - - - o - - - o B
      |  *:::::::::::::*      |
      |     *:::::::::::*     |
      |        *:::::::::*    |
    x |           *:::::::*   | x
      |              *:::::*  |
      |                 *:::* |
      |                    *:*|
    D o - - - - - - - - - - - o C
                 15

The length of the rectangle is 15.
The width of the rectangle is

The area of
The area of rectangle

The fraction (ratio) is: .

2. and are midpoints of sides and of square
What is the ratio of the area of to the area of the square?

Make a sketch and the answer is obvious . . .

Code:

              N
    A o - - - o - - - o B 
      |:::::* | *     |
      |:::*   |   *   |
      |:*     |     * |
    M o - - - + - - - *
      | *     |     * |
      |   *   |   *   |
      |     * | *     |
    D o - - - * - - - o C