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.
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
APPEARS IN
RELATED QUESTIONS
A triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
Find the area of an equilateral triangle having altitude h cm.
If each side of a triangle is doubled, the find percentage increase in its area.
If each side of a equilateral triangle is tripled then what is the percentage increase in the area of the triangle?
The sides of a triangle are 11 m, 60 m and 61 m. The altitude to the smallest side is
The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is
The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area 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 ______.
The area of the equilateral triangle is `20sqrt(3)` cm2 whose each side is 8 cm.
