Home
Class 9
MATHS
Find the area of a trapezium whose paral...

Find the area of a trapezium whose parallel sides `25 c m ,13 c m` and other sides are `15 cm and 15 cm`

Text Solution

Verified by Experts

Let ABCD be the given trapezium whose AB=25 cm, CD = 13, BC = 15 cm and AD = 15 cm.
Draw `" "` CE||AD
Now, ADCE is a parallelogram in which AD|| CE and AE||CD.
`:." " AE=DC=13` cm,
and BE=AB-AE=25-13=12 cm
In `DeltaBCE, s=(15+15+12)/(2)=21 `cm
`:." "` Area of `DeltaBCE=sqrt(s(s-a)(s-b)(s-c))`
`=sqrt(21(21-15)(21-15)(21-12))`
`=sqrt(21xx6xx6xx9)=18 sqrt(21) "cm"^(2) " " ...(1)`
Let h be the height of `DeltaBCE`, then
Area of `DeltaBCE=(1)/(2)("base"xx"height")`
`=(1)/(2)xx12xxh=6h " " (.:' EB=12)" " ...(2)`
From (1) and (2) , we have
`6h=18sqrt(21)`
`h=3sqrt(21)`cm
The height trapezium ABCD is same as that of `DeltaBCE`.
`:. ` Area of trapezium `=(1)/(2) (AB+CD)xxh`
`=(1)/(2)(25+13)xx3sqrt(21)=57sqrt(21) "cm"^(2)`.
Promotional Banner

Topper's Solved these Questions

  • HERONS'S FORMULA

    NAGEEN PRAKASHAN ENGLISH|Exercise Problems From NCERT / Exemplar|10 Videos

  • HERONS'S FORMULA

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 12a|11 Videos

  • CONSTRUCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISE|36 Videos

  • INTRODUCTION TO EUCLID'S GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|8 Videos

Similar Questions

Explore conceptually related problems

Find the area of a trapezium whose parallel sides 25 c m ,13 c m and other sides are 15 c ma n d15 c mdot

Find the area of a trapezium whose parallel sides are 20cm and 10cm and other sides are 13cm and 13cm

A field is in the shape of a trapezium whose parallel sides are 25m and 10 m. The non-parallel sides are 14m and 13m. Find the area of the field.

A field is in the shape of a trapezium whose parallel sides are 25m and 10 m. The non-parallel sides are 14m and 13m. Find the area of the field.

Find area of a trapezium whose parallel sides are 28 cm and 14 cm and the distance between them is 5 cm. .

Find the area of a triangle whose sides are 13 c m ,14c m ,15cm

Find the area of a triangle whose sides are 13 c m ,14c m ,15cm

Find the area of the trapezium whose parallel sides are 15 cm amd 23 cm, whereas the non-parallel sides are 10 cm and 8 cm.

Find the altitude of a trapezium whose area is 65\ c m^2 and whose bases are 13cm and 26cm.

Find the area of a trapezium whose parallel sides are of lengths 10cm and 12cm and the distance between them is 4cm.