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प्रश्न
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 ______.
पर्याय
`1/2` ar (ABC)
- `1/3` ar (ABC)
- `1/4` ar (ABC)
- ar (ABC)
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उत्तर
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) `
संबंधित प्रश्न
In the below fig. OCDE is a rectangle inscribed in a quadrant of a circle of radius 10 cm. If
OE = 2√5, find the area of the rectangle.
ABCD is a parallelogram in which BC is produced to E such that CE = BC. AE intersects
CD at F.
(i) Prove that ar (ΔADF) = ar (ΔECF)
(ii) If the area of ΔDFB = 3 cm2, find the area of ||gm ABCD.
In the below fig. X and Y are the mid-points of AC and AB respectively, QP || BC and
CYQ and BXP are straight lines. Prove that ar (Δ ABP) = ar (ΔACQ).
PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then find ar (ΔRAS)
The median of a triangle divides it into two ______.
If AD is median of ΔABC and P is a point on AC such that
ar (ΔADP) : ar (ΔABD) = 2 : 3, then ar (Δ PDC) : ar (Δ ABC)
Find the area of a square, whose side is: 4.1 cm.
So the area of piece A = ________ square cm
Find the area of the following figure by counting squares:
Find the area of the following figure by counting squares:
