Geometry Area of sections of a parallelogram

In summary, the area of a parallelogram is 60 square units and a segment is drawn from one vertex to the midpoint of an opposite side. The diagonal is drawn between the other two vertices, creating four regions. By splitting region IV into two triangles and using the ratio of the similar triangles formed, it can be determined that regions I, II, III, and V have areas of 5, 10, 20, and 25 units respectively. With the help of geometrical techniques, this can be verified without using a tool like Geometer Sketchpad.
  • #1
Wildcat
116
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1. The area of a parallelogram is 60 square units. A segment is drawn from one vertex to the midpoint of an opposite side. The diagonal is drawn between the other two other vertices. Find the area of the four regions formed.

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3. I found that two of the triangles formed are similar so the ratio of those triangles would be 1/4. The diagonal separates one region into two triangles which would total 30 units and the lower portion made up of a quadrilateral and a triangle would total 30 units. I'm stuck. I can't find another relationship. Help!

OK I constructed the diagram on geometer sketchpad and found the areas, but I'm wondering how it can be done without geometer sketchpad?? region I = 5 region II=10 region III = 20 and region IV (quadrilateral) = 25. Any ideas??
 
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  • #2
Hi Wildcat! :smile:

Hint: split region IV into triangles V and VI, and find relations between I II III and V :wink:
 
  • #3
tiny-tim said:
Hi Wildcat! :smile:

Hint: split region IV into triangles V and VI, and find relations between I II III and V :wink:

I did that. And I know from what I did on GSP that One of the triangles say V is congruent to II, but I can't figure out why. Can you give me another hint :)
 
  • #4
forget congruence, think areas :wink:
 
  • #5
tiny-tim said:
forget congruence, think areas :wink:

Thanks, I finally got it :)
 

FAQ: Geometry Area of sections of a parallelogram

What is the formula for finding the area of a parallelogram?

The formula for finding the area of a parallelogram is A = b x h, where A represents the area, b represents the length of the base, and h represents the height.

How do you find the height of a parallelogram?

To find the height of a parallelogram, you can use the formula h = A/b, where h represents the height, A represents the area, and b represents the length of the base.

Can the area of a parallelogram be negative?

No, the area of a parallelogram cannot be negative. It is always a positive value, as it represents the amount of space inside the shape.

What is the difference between a parallelogram and a rectangle?

A parallelogram and a rectangle are both quadrilaterals, meaning they have four sides. However, a rectangle has four right angles and two pairs of equal sides, while a parallelogram has two pairs of parallel sides and opposite angles are equal.

How do you find the area of a section of a parallelogram?

To find the area of a section of a parallelogram, you can divide the parallelogram into smaller shapes (such as triangles or rectangles) and use their respective area formulas. Then, add the areas of the smaller shapes together to find the total area of the section.

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