SOLUTION: When the midpoints of the consecutive sides of a rectangle are joined in order, a rhombus is formed. Find the ratio of the areas of the rhombus and the rectangle. Please explain.

Question 1115064: When the midpoints of the consecutive sides of a rectangle are joined in order, a rhombus is formed. Find the ratio of the areas of the rhombus and the rectangle.
Please explain. Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Let's draw out the picture. Start with rectangle ABCD (red points). Then plot the midpoints of the rectangle sides. These are points E, F, G, H (blue points). Connecting the blue points forms the rhombus EFGH. The dashed lines are the diagonals. Notice how the diagonals are the same length as the base and height of the rectangle ABCD.

Let's say the base of the rectangle is b and the height is h. The area is therefore b*h

For the rhombus, one of the diagonals is b units long, while the other is h units long. The area of any rhombus is equal to the product of the diagonals over 2. So its (b*h)/2

The ratio of the two areas b*h and (b*h)/2 is 1:1/2 or 2:1, where the area of the rectangle is listed first. In other words, the rectangle is twice as big as the rhombus. Put another way, the rhombus area is half that of the rectangle area.

Example: If the rectangle has an area of 10, then the rhombus will have an area of 5.

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