Consider the area of the following solids:
(A) A rhombus whose diagonals are 48 cm and 20 cm long.
(B) A trapezium with parallel sides 9.7 cm and 6.3 cm, and the distance between them is 6.5 cm.
(C) A parallelogram with a base equal to 25 cm and the corresponding height measuring 16.8 cm.
(D) A rhombus, whose diagonals are 30 cm and 16 cm.
Arrange the above in ascending order.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B), (D), (C), (A)
Each area comes from its own formula: a rhombus is half the product of its diagonals, a trapezium is half the sum of the parallel sides times the distance between them, and a parallelogram is base times height.
(A) Rhombus — \(\displaystyle\frac{1}{2}\times48\times20=480\,\mathrm{cm^2}\)
(B) Trapezium — \(\displaystyle\frac{1}{2}\times(9.7+6.3)\times6.5=8\times6.5=52\,\mathrm{cm^2}\)
(C) Parallelogram — \(25\times16.8=420\,\mathrm{cm^2}\)
(D) Rhombus — \(\displaystyle\frac{1}{2}\times30\times16=240\,\mathrm{cm^2}\)