Question

the perimeter of a trapezium is 104m it's non parallel sides are 18m and 22m and it's altitude is 16m.Find the area of trapezium​

Answer 1

$\huge\underline\mathrm{SOLUTION:-}$

AnswEr:

Area of the trapezium = 512 m²

Given Information:

The Perimeter of the trapezium = 104 m

Non parallel sides are 18 m and 22 m

Altitude = 16 m

Need To Find :

Area of the Trapezium = ?

$\underline\mathtt\green{ExPlanation:-}$

Let the sum of parallel sides be x.

Formula used here:

$\boxed{ \sf \: Perimeter = Sum \: of \: all \: sides}$

Putting the values we get:

$\longrightarrow \sf \: 104 = 18 + 22 + x$

$\longrightarrow \sf \: 104 = 40 + x$

$\longrightarrow \sf \: x = 64$

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Now need to find:

• The area of the trapezium = ?

Formula used here:

$\bigstar \: \boxed{ \sf \: Area_ {Trapezium } = \dfrac{1}{2} \times Sum \: of \: parallel\: sides \times height}$

Putting the values we get:

$\longrightarrow \sf \: Area = \: \dfrac{1}{2} \times 64\times 16$

$\longrightarrow \sf \: Area = \dfrac{1}{2} \times 64 \times 8$

$\longrightarrow \sf \red{ \sf \:Area = 512 {m}^{2} }$

ThereFore:

Area of the trapezium is 512 m²

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Answer 2

Given:

Perimeter of Trapezium=104m

Non parallel sides are 22m and 18m

Let X and Y be the parallel sides of trapezium.

Altitude=16m

Perimeter of trapezium = X+Y+22+18

104=X+Y+40

X+Y=104-40

X+Y=64

Area of trapezium = 1/2 ( sum of parallel side)× altitude

=1/2 (X+Y)×16

=(1/2)64×16

=512 m^2

Therefore Area of Trapezium is 512m^2.