Match List-I with List-II

List-I	List-II
(Shapes)	(Area/Perimeter/Diagonal/slant height)
(A) Trapezium	(I) √(l² + b² + h²)
(B) Sector of a circle	(II) √(R² + (R - r)²)
(C) Cuboid	(III) 1/2 h(a + b)
(D) Frustum of cone	(IV) (θ/360°) × 2πr

Choose the correct answer from the options given below:

(A) Trapezium → (III) $\frac{1}{2} h(a + b)$

This is the area formula of a trapezium. A trapezium has two parallel sides $a$ and $b$, with $h$ as the perpendicular height between them.

Area $= \frac{1}{2} \times h \times (a + b)$

(B) Sector of a circle → (IV) $\frac{\theta}{360°} \times 2\pi r$

This is the arc length (perimeter) of a sector. A sector is a portion of a circle with angle $\theta$ (in degrees) and radius $r$. The full circumference is $2\pi r$.

Arc length $= \frac{\theta}{360°} \times 2\pi r$

The fraction $\frac{\theta}{360°}$ represents what portion of the full circle the sector occupies.

(C) Cuboid → (I) $\sqrt{l^2 + b^2 + h^2}$

This is the diagonal of a cuboid (3D box), where $l$ is length, $b$ is breadth, and $h$ is height.

Diagonal $= \sqrt{l^2 + b^2 + h^2}$

This is the 3D extension of the Pythagorean theorem, giving the distance from one corner to the opposite corner through the interior.

(D) Frustum of cone → (II) $\sqrt{R^2 + (R - r)^2}$

This represents the slant height relationship in a frustum of a cone. A frustum is a cone with the top cut off, where $R$ is the radius of the larger base and $r$ is the radius of the smaller base.

The correct matching is:

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)