If a triangle and a parallelogram are on the same base and between the same parallels

Question:

If a triangle and a parallelogram are on the same base and between the same parallels, then the ratio of the area of the triangle to the area of the parallelogram is

(a) 1 : 2
(b) 1 : 3
(c) 1 : 4
(d) 3 : 4

Figure

 

Solution:

(a) 1:2

If a triangle and a parallelogram are on the same base and between the same parallels, then the area of the triangles is half the area of the parallelogram.

i.e., area of triangle $=\frac{1}{2} \times$ area of parallelogram

$\therefore$ Required ratio = area of triangle : area of parallelogram $=\frac{1}{2}: 1=1: 2$

 

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