Question

The area of a trapezium with equal non-parallel sides is 168 mº. If the lengths
of the parallel sides are 36 m and 20 m, find the length of each non-parallel
side.​

Answer 1

$\bf{\huge{\underline{\boxed{\tt{\blue{Answer:}}}}}}$

Gívéñ :-

• Area of trapezium = 168 m²
• Length of one of the parallel side = 36 m
• Length of the other parallel side = 20 m

Tó Fîńd :-

• Length of each non parallel sides
• Height of the trapezium

Sóĺúťíóń :-

Area of trapezium is given by the formula,

$\bf{\large{\underline{\boxed{\tt{Area\:of\:trapezium\:=\:1/2\:(Sum\:of\:parallel\:sides\:)(height) }}}}}$

Plug in the values,

168 = $\bf\large\frac{1}{2}$ (36 + 20) × h

168 × 2 = 56 × h

336 = 56 × h

$\bf\large\frac{336}{56}$ = h

6 = h

Height of the trapezium = 6 m

Now, we have to find the length of the non parallel sides.

As per the figure,

ΔPTQ is a right angled triangle,

where, m $\angle{PTQ}$ = 90°, PQ is the hypotenuse and QT and PT are two sides of the triangle.

•°• By Pythagoras Theorem,

PQ² = QT² + PT²

Plug in the values,

PQ² = 8² + 6²

PQ² = 64 + 36

PQ² = 100

PQ = √ 100

PQ = 10 m

Length of one parallel side of the trapezium, PQ = 10 m

Length of SR = 10 m

°•° As PQ and SR. Since, the two non parallel sides of the trapezium are congruent we infer that it is an isosceles trapezium.

•°• Length of non parallel sides of the trapezium are 10 m each.