Question

Assertion (A): A trapezium with parallel sides 8 cm and 12 cm, and height 5 cm, has an area of 100 cm². Reason (R): Area of a trapezium = \frac{1}{2}\times (sum of parallel sides) \times height.

A field is in the shape of a trapezium. Its parallel sides are 25 m and 15 m and the perpendicular distance between them is 12 m. Find the area of the field in m².

The pentagon ABCDE in the figure is made of a rectangle ABCE (8 cm by 6 cm) and a triangle ECD. The height of D above EC is 3 cm. Find the area of the pentagon in cm².

A surveyor measures a field ABCDE using a baseline AD = 18 m (see figure). On the right of AD: BP = 6 m with AP = 5 m, and CQ = 8 m with AQ = 12 m. On the left: ER = 8 m with AR = 10 m. All offsets are perpendicular to AD. Find the area of the field in m².