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19 Jul 2023, 22:17
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Bunuel KarishmaB
I solved the question correctly by applying a concept I know about inscribed triangles within rectangles (reasoned that parallelograms are also regular figures) but I'd appreciate your validation.
Concept: If a triangle inscribed in a rectangle shares a side with the rectangle, the area of the triangle is equal to half the area of the rectangle. In other words, the area of the two smaller triangles = area of main triangle.
Applying this rule to the parallelogram, I connected points E and C to create an inscribed triangle.
First small triangle / Main triangle + second small triangle = 1 / 3
Screenshot 2023-07-20 at 10.41.10 AM.png [ 1002.36 KiB | Viewed 1073 times ]
I solved the question correctly by applying a concept I know about inscribed triangles within rectangles (reasoned that parallelograms are also regular figures) but I'd appreciate your validation.
Concept: If a triangle inscribed in a rectangle shares a side with the rectangle, the area of the triangle is equal to half the area of the rectangle. In other words, the area of the two smaller triangles = area of main triangle.
Applying this rule to the parallelogram, I connected points E and C to create an inscribed triangle.
First small triangle / Main triangle + second small triangle = 1 / 3
Attachment:
Screenshot 2023-07-20 at 10.41.10 AM.png [ 1002.36 KiB | Viewed 1073 times ]
20 Jul 2023, 09:24
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achloes
You are absolutely correct. Why? The reasoning is given in my post here: https://gmatclub.com/forum/in-the-figur ... l#p3153698
Area of a rectangle = Base * Height
Area of triangle with same Base = (1/2) * Base * Height
Note that when the vertex of the triangle lies on the opposite side to the base, the height of both is the same.
Exactly the same concept is applicable to the parallelogram too. Area of parallelogram is also base * height.
30 Aug 2023, 23:31
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Quad BCDE is a trapezium. The area of a trapezium is the average of the bases * height. That is (BC + ED)/2 * height.
The area of the triangle is 1/2 * AE * height.
Area of triangle/ area of trapezium = (1/2 * AE * height) / ((BC + ED)/2 * height)
Cancel out the height as they both are equal.
= AE/BC+ED = AE/3AE = 1/3
The area of the triangle is 1/2 * AE * height.
Area of triangle/ area of trapezium = (1/2 * AE * height) / ((BC + ED)/2 * height)
Cancel out the height as they both are equal.
= AE/BC+ED = AE/3AE = 1/3
