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27.05.2021, adminIn such a case, write the common base and the two parallels. Solution: The figures i , iii and v lie on the same base and between the same parallels.
If a triangle and a parallelogram are on the same base and between the same parallels, then A E U the area of the triangle is equal to half the area of the parallelogram. A farmer was having a field in the form of a parallelogram PQRS. In how many parts the fields is divided?
What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately.
How should she do it. Join AP and AQ. Clearly, the field is divided into three parts i. Let us join B and E. Since, a median divides the triangle into two triangles of equal area. Show that the diagonals of a parallelogram divide it into four triangles of equal area. Show that i BDEF is a parallelogram. Prove that DE BC.
Hence, DE BC. ABCD is a parallelogram [Given] and AC is its diagonal, we know that diagonal of a parallelogram divides it into two triangles of equal areas.
Since, triangles on the same base and between the same parallels have equal areas. A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre.
Itwaari agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented. Let us join CX. Prove that ABCD is a trapezium. Since, the triangles are on the same base and having equal area.
So, ABCD is a trapezium. So, DC RP i. So, AB DC i. Show that the perimeter of the parallelogram is greater than that of the rectangle. Let us join AC. We know that triangles on the same base and between the same parallels are equal in area. Also, R is the mid-point of AP. In figure, ABC is a right triangle right angled at A. ACFG � 5. ACFG [From vi part].
Common base Two parallels Fig. ABCD Ex 9. ACFG � 5 vii We have ar quad. RD Sharma Class 12 Solutions. Watch Youtube Videos.
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