Advertisements
Advertisements
Question
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
Advertisements
Solution
Draw a line BE parallel to AD and draw a perpendicular BF on CD.
It can be observed that ABED is a parallelogram.
BE = AD = 13 m
ED = AB = 10 m
EC = 25 − ED = 15 m
For ΔBEC,
Semi-perimeter,
`s=(13+14+15)/2=21 m`
By Heron’s formula,
`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`
`"Area of ΔBEC "=[sqrt(21(21-13)(21-14)(21-15))]m^2`
`=[sqrt(21(8)(7)(6))]m^2`
= 84 m2
`"Area of ΔBEC "=1/2xxCExxBF`
`rArr84=1/2xx15xxBF`
`rArrBF=168/15=11.2 m`
Area of ABED = BF × DE = 11.2 × 10 = 112 m2
Area of the field = 84 + 112 = 196 m2
RELATED QUESTIONS
A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
A park, in the shape of a quadrilateral ABCD, has ∠C = 900, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m How much area does it occupy?
Two parallel side of a trapezium are 60 cm and 77 cm and other sides are 25 cm and 26 cm. Find the area of the trapezium.
Mark the correct alternative in each of the following:
The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is
In the given figure, the ratio AD to DC is 3 to 2. If the area of Δ ABC is 40 cm2, what is the area of Δ BDC?
If the length of a median of an equilateral triangle is x cm, then its area is
If every side of a triangle is doubled, then increase in the area of the triangle is
A square and an equilateral triangle have equal perimeters. If the diagonal of the square is \[12\sqrt{2}\] cm, then area of the triangle is
The length of each side of an equilateral triangle having an area of `9sqrt(3)`cm2 is ______.
If the area of an equilateral triangle is `16sqrt(3)` cm2, then the perimeter of the triangle is ______.
