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  • If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of parallelogram is (A) 1 : 3 (B) 1 : 2 (C) 3 : 1 (D) 1 : 4

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

(A) 1 : 3
(B) 1 : 2
(C) 3 : 1
(D) 1 : 4

Answers (1)

best_answer

Answer: [B]

Solution.

We know that a triangles and a parallelogram are on the same base and between the same parallels, then the area of the triangle is equal to half the area of the parallelogram. Let us prove the same.We have a parallelogram ABCD and triangle BEC on the same base BC.

 

Construct EM perpendicular to BC
Area of a triangle is given as: \frac{1}{2} (Base) (Height)
Area of  \triangle BEC=\frac{1}{2}(BC)(EM)     …(i)
 

Area of a parallelogram is given as: (Base) (corresponding altitude)
Area of a parallelogram ABCD= (BC) (EM) …(ii)
Ratio of the area of the triangle to the area of parallelogram = (i) : (ii)
=\frac{1}{2}(BC)(EM)/(BC)(EM)
=\frac{1}{2}
Hence the ratio of the area of the triangle to the area of parallelogram is 1 : 2.
Hence, (B) is the correct answer.

 

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