Question

Perimeter of a trapezium is 116m.Non parallel sides are 16m and 24m respectively. Altitude is 16m Find area of Trapezium

Answer 1

this is ur answer ,,

Answer 2

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

AnswEr:

• Area of the trapezium = 608 m²

Given Information:

• Perimeter of the trapezium = 116 m
• Non parallel sides are 16 m and 24 m
• Altitude = 16 m

Need To Find :

• Area of the Trapezium = ?

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

Let the parallel sides of the trapezium be x and y.

Formula used here:

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

Putting the values according to the given formula:

$\longrightarrow \sf \: 116 = 16 + 24 + x + y$

$\longrightarrow \sf \: 116 =40 + x + y$

$\longrightarrow \sf \: 116 - 40 = x + y$

$\longrightarrow \sf \: 76= x + y$

$\longrightarrow \red{\sf \:x + y = 76}$

Hence:

• The sum of parallel sides is 76 m

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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 according to the given formula:

$\longrightarrow \sf \: Area = \: \dfrac{1}{2} \times (x + y) \times h$

$\longrightarrow \sf \: Area = \dfrac{1}{2} \times 76 \times 16$

$\longrightarrow \sf \: Area = \cancel \dfrac{1216}{2}$

$\longrightarrow \sf \red{ \sf \:Area = 608 {m}^{2} }$

Hence:

• Area of the trapezium is 608 m²

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