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Question
The mid-points of the sides of a triangle ABC along with any of the vertices as the fourth point make a parallelogram of area equal to ______.
Options
`1/2` ar (ABC)
- `1/3` ar (ABC)
- `1/4` ar (ABC)
- ar (ABC)
Solution
The mid-points of the sides of a triangle ABC along with any of the vertices as the fourth point make a parallelogram of area equal to `underlinebb(1/2 ar (ABC))`.
Explanation:
Given: ABCD is a triangle.
Mid points of the sides of ΔABC with any of the vertices forms a parallelogram.
To find: Area of the parallelogram
Calculation: We know that, Area of a parallelogram = base × height
Hence area of || gm DECF = EC × EG
area of || gm DECF = EC × EG
area of || gm DECF = `1/2 BC xx 1/2 AE` ...(E is the midpoint of BC)
area of || gm DECF = `1/2(1/2BC xx AE)`
area of || gm DECF = `1/2(ar ( ΔABC) `
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