Advertisements
Advertisements
Question
Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.
Advertisements
Solution
AB = DE
EC = BC − BE
EC = (48 − 40) m
EC = 8 m
In Δ DEC,
(DE)2 + (EC)2 = (D C)2
(DE)2 + (8)2 = (17)2
(DE)2 = (17)2 − (8)2
DE = 289 − 64
DE = 225 m2
DE = `sqrt225` m
DE = 15 m
AB = 15 m
Area of trapezium, ABCD
`= 1/2` × (sum of parallel sides) × Height
`= 1/2` × (AD + BC) × AB
`1/2` × (40 + 48) ×15
= 660m2
RELATED QUESTIONS
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.
Find the altitude of a trapezium whose area is 65 cm2 and whose bases are 13 cm and 26 cm.
The area of a trapezium is 91 cm2 and its height is 7 cm. If one of the parallel sides is longer than the other by 8 cm, find the two parallel sides.
The area of a trapezium is 1586 cm2 and the distance between the parallel sides is 26 cm. If one of the parallel sides is 38 cm, find the other.
Find the area of the field shown in Fig. 20.39 by dividing it into a square, a rectangle and a trapezium.
Find the area of the pentagon shown in fig. 20.48, if AD = 10 cm, AG = 8 cm, AH = 6 cm, AF = 5 cm, BF = 5 cm, CG = 7 cm and EH = 3 cm.
Find the area enclosed by each of the following figures [Fig. 20.49 (i)-(iii)] as the sum of the areas of a rectangle and a trapezium:
The area of a trapezium is 279 sq.cm and the distance between its two parallel sides is 18 cm. If one of its parallel sides is longer than the other side by 5 cm, find the lengths of its parallel sides.
The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is ______.
A trapezium with 3 equal sides and one side double the equal side can be divided into ______ equilateral triangles of ______ area.
