On the same base and with the same altitude, consider a parallelogram (area P), a triangle (area R), and a rectangle (area A). Which relation is always true?
Aptitude
Area
Difficulty: Easy
Choose an option
-
AP=R
-
BP=A
-
CP=A/2
-
DP=2R
Answer
Correct Answer: P=2R
Explanation
Introduction / Context:For plane figures sharing the same base length b and altitude h, their areas follow standard formulas: parallelogram P = b*h, rectangle A = b*h, triangle R = (1/2)*b*h. Comparing these immediately yields the fixed relations among P, A, and R.
Given Data / Assumptions:
- All figures share base b and altitude h.
Concept / Approach:Write each area in terms of b and h and compare.
Step-by-Step Solution:
Parallelogram: P = b * hRectangle: A = b * hTriangle: R = (1/2) * b * hTherefore P = A and P = 2R, so in particular P = 2R.Why Other Options Are Wrong:
- P=R: False; triangle area is half.
- P=A/2: False; parallelogram equals rectangle, not half.
Final Answer:P=2R