Match List I with List II
| List I | List II | ||
|---|---|---|---|
| A. |  | I. | \(\pi r^{2}\) |
| B. |  | II. | \(\frac{1}{2}\times\text{base}\times\text{height}\) |
| C. |  | III. | \(\frac{1}{2}\times d_{1}\times d_{2}\) |
| D. |  | IV. | \(\frac{1}{2}\times(a+b)\times h\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A-II, B-III, C-IV, D-I
Each figure is matched with the area formula of its shape, read from the parts marked on it.
A. Triangle (base and height marked) — this matches II. \(\frac{1}{2}\times\text{base}\times\text{height}\). A triangle is half of a parallelogram on the same base and of the same height.
B. Rhombus (diagonals \(d_1\) and \(d_2\) marked) — this matches III. \(\frac{1}{2}\times d_1\times d_2\). The diagonals of a rhombus cut each other at right angles, so they split it into four right triangles whose areas add up to half the product of the diagonals.
C. Trapezium (parallel sides \(a\), \(b\) and height \(h\) marked) — this matches IV. \(\frac{1}{2}\times(a+b)\times h\), half the sum of the parallel sides times the distance between them.
D. Circle (radius \(r\) marked) — this matches I. \(\pi r^2\).