Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.
Given: Perpendicular distance
= 100 m
Area of the trapezium shaped field
= 10500 m2
Let side along the road be x m and side along the river = 2x m
Area of the trapezium field
= 1/2 (a+b)h
⇒ 10500 = = 1/2 (x + 2x) × 100
⇒x = 70m
Hence the side along the river =
= 2 × 70 = 140 m.
Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.