Triangle and Parallelogram of Same Base and Between the Same Parallels


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The parallelograms are on the same base and between the same parallels.
Area of a Parallelogram = b × h
In both parallelograms:
•    The bases are equal.
•    The heights are equal.
Area of parallelogram ABCD = Area of parallelogram ABGH.
Parallelograms on the same base and between the same parallels are equal in area.
Prove that the area of the triangle is equal to half the area of the parallelogram, if they are on the same base and are between the same parallels.

Δ ABP and  parallelogram ABCD are on same base AB and between the same parallels AB and PC.
To Prove: ar (ΔABP) =1/2 ar ( ||gm ABCD)
Construction: Draw BQ || AP
ar ( ||gm ABQP) = ar ( || gm ABCD (Parallelograms on the same base and between the same parallels are equal in area.) 
ar (Δ ABP) = ar (Δ BQP)
ar (Δ ABP) =  (½) ar (|| gm ABQP)
ar (Δ ABP) =  (½) ar (|| gm ABCD).

1 . Three squares are joined at there corners and strung between two vertical poles as shown. Find the value of x.

Recall that sum of angles of a polygon = (2n - 4) × 90°
Here number of sides, n = 9
Hence the sum of angles of the given pol...

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Length = 21 cm
Breadth = 9 cm
width = 8 cm

Surface Area of tin box (excluding lid)
= 2(bh+hl) + lb...

3 . formula for area of equilateral triangle

root3/4 a suare

4 . Find the height of the parallelogram.

Perimeter of triangle = ( a + b + c) = (26 + 28 + 30) cm = 84 cm
2 s = 84 cm
s = 42 cm,a =...

5 . find the area of figure.All corners are right angles.AB= 4 [int]1/4,BC=2[int]3/4,DE=3[int]1/2,EF=4,FG=4[int]1/2...

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