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

Let the sum of parallel sides be x

perimeter = sum of all sides

104 = 18 + 22 + x

104 = 40 + x

x = 64

as we know that

area of trapezium = 1/2 × sum of parallel sides × altitude

= 1/2 × 64 × 16

= 64 × 8

= 512 cm^2

so area of trapezium is 512 cm^2

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 = ?

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

Let the sum of parallel sides be x.

Formula used here:

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

Putting the values according to the given formula:

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

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

$\longrightarrow \sf \: x = 64$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

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:

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

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

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

Hence:

• Area of the trapezium is 512 m²

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