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Triangle and Parallelogram of Same Base and Between the Same Parallels

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HD 3:51 Animated video Lecture for 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.
Theorem: 
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.

Given:
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
Proof:
ar ( ||gm ABQP) = ar ( || gm ABCD (Parallelograms on the same base and between the same parallels are equal in area.) 
Δ ABP ≅ Δ BQP
ar (Δ ABP) = ar (Δ BQP)
ar (Δ ABP) =  (½) ar (|| gm ABQP)
ar (Δ ABP) =  (½) ar (|| gm ABCD).

Questions & Answers

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...
3 . 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...
Given question is not clear please send us the exact question so that we can provide the solution at the earliest.
4 . Find the height of the parallelogram.
Sol:
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 in which all corners are right angles
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