Find the area of the trapezium above and calculate the area of the sector of the arc.

The parallel sides are $a = 7 \text{ cm}$ and $b = 13 \text{ cm}$.
The perpendicular height is $h = 8 \text{ cm}$.

The correct option is B.
The area of the trapezium is $\boxed{\text{B. } 80 \text{ cm}^2}$.

37. A circular arc subtends angle $150^\circ$ at the centre of a circle of radius $12 \text{ cm}$, calculate the area of the sector of the arc.

Angle $\theta = 150^\circ$.
Radius $r = 12 \text{ cm}$.

The correct option is D.
The area of the sector is $\boxed{\text{D. } 60 \pi \text{ cm}^2}$.

38. Calculate the volume of a cuboid of length $0.76 \text{ cm}$, breadth $2.6 \text{ cm}$ and height $0.82 \text{ cm}$.

Length $l = 0.76 \text{ cm}$.
Breadth $b = 2.6 \text{ cm}$.
Height $h = 0.82 \text{ cm}$.

Rounding to two decimal places, $V \approx 1.62 \text{ cm}^3$.
The correct option is A.
The volume of the cuboid is $\boxed{\text{A. } 1.62 \text{ cm}^3}$.

39. The locus of a point equidistant from the intersection of lines $3x - 7y + 7 = 0$ and $4x - 6y + 1 = 0$ is a

The intersection of two distinct lines is a single point.
The locus of a point equidistant from a single fixed point is a circle, with the fixed point as its center.
The correct option is C.
The locus of a point equidistant from the intersection of lines $3x - 7y + 7 = 0$ and $4x - 6y + 1 = 0$ is a $\boxed{\text{C. Circle}}$.

40. The gradient of the straight line joining the points P $(5, -7)$ and Q $(-2, -3)$ is

Point P: $(x_1, y_1) = (5, -7)$.
Point Q: $(x_2, y_2) = (-2, -3)$.

The correct option is C.
The gradient of the straight line joining the points P $(5, -7)$ and Q $(-2, -3)$ is $\boxed{\text{C. } -\frac{4}{7}}$.