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Assertion (A): The area of a triangle is half the area of a parallelogram on the same base and between the same parallels. Reason (R): A diagonal of a parallelogram divides it into two congruent triangles. Which is correct?

Class 7Perimeter and AreaPerimeter and Area
  • ABoth A and R are true, and R is the correct explanation of A
  • BBoth A and R are true, but R is not the correct explanation of A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

A diagonal splits a parallelogram into two congruent triangles, so each triangle is half the parallelogram. R correctly explains A.
Answer: A) Both A and R are true, and R is the correct explanation of A

Key idea: Triangle area

**Area of a triangle = ½ × base × height.**

The base is any side you choose; the height is the perpendicular distance from that base to the opposite vertex (NOT the slant length of another side). For a right triangle, the two legs that meet at the right angle ARE the base and height.

Example: triangle with base 6 cm and height 4 cm. Area = ½ × .

The perimeter of a triangle is just the sum of its three sides — no formula needed.

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