Question

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.

ABCDEF is a hexagon with AB = CD = DE = FA = 10 cm and BC = FE = 12 cm. The diagonal AD is 24 cm, and BC and FE are each 8 cm away from AD (see figure). Find the area of the hexagon in two ways: (i) by splitting it into two trapeziums along AD, (ii) by splitting it into rectangle BCEF and two triangles ABF and CDE.

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.

The residents of a colony in Jaipur have a park shaped like a trapezium. Its parallel sides are 40 m and 28 m, and they are 15 m apart. In the middle there is a rhombus-shaped flower bed whose diagonals are 8 m and 6 m. The rest of the park is to be covered with grass.