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

Answer: Answer is in the attachment...

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Answer 2

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

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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