Q. 144.4( 20 Votes )

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.

Answer :

Given: Parallel sides of trapezium = 25 m and 10 m

Non – parallel sides of trapezium = =14 m and 13 m


To Find: Area of the field


Concept Used:


If sides of a triangle are a, b, and c, then area of a triangle is given by:



Where s = semiperimeter of the triangle



Diagram:



Construction:


From C, draw CE || DA.


Explanation:


Now, we can see that ADCE is a parallelogram in which AE || CD and AD || CE.


Now, we can get,


AE = 10 m and CE = 13 m


BE = AB – AE [From the figure]


Therefore,


BE = 25 m – 10 m = 15 m


Now Area of trapezium = Area of Parallelogram AECD + Area of triangle ECB


Let us first calculate the area of a triangle,




s = 21 m





Area = 3 × 7 × 4 m2


Area of Δ ECB = 84 m2


We also know that Area of Δ ECB = 1/2 (BE × CL)


84 = 1/2 (15 × CL)


15 × CL = 168


CL


CL = Height of the parallelogram


Now, Area of parallelogram ADCE = Base × Height


Area of parallelogram = 112 m2


Hence, Area of Trapezium ABCD = (84 + 112) m2 = 196 m2.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Heron's FormulaHeron's FormulaHeron's Formula43 mins
Champ Quiz | Know About Heron's FormulaChamp Quiz | Know About Heron's FormulaChamp Quiz | Know About Heron's Formula53 mins
Heron's formulaHeron's formulaHeron's formula32 mins
Champ Quiz | Heron's FormulaChamp Quiz | Heron's FormulaChamp Quiz | Heron's Formula41 mins
Quiz | Heron's FormulaQuiz | Heron's FormulaQuiz | Heron's Formula44 mins
NCERT | Heron's FormulaNCERT | Heron's FormulaNCERT | Heron's Formula49 mins
Quiz | Heron's FormulaQuiz | Heron's FormulaQuiz | Heron's Formula45 mins
Quiz | Herons FormulaQuiz | Herons FormulaQuiz | Herons Formula44 mins
NCERT | Important Qs. on Herons FormulaNCERT | Important Qs. on Herons FormulaNCERT | Important Qs. on Herons Formula42 mins
Champ Quiz | Area of TriangleChamp Quiz | Area of TriangleChamp Quiz | Area of Triangle53 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :