Question

the parallel sides of a trapezim are 25cn and 13 cm and the oter sides are equal. find the length of non parallel sides if the area of trapezium is 57√21cm ^2

Answer 1

Area of trapezium= 1/2*d*(a+b) sq. Units.

Where d= perpendicular distance between parellel sides which are a & b respectively, 25 &13 cm.

25–13=12, 12/2= 6 cm is base of RT. Angled ∆.

Non parallel sides=10cm, this is hypotenuese of this ∆.

Find ‘d ‘ to solve.

d=√{10^2–6^2}=8 cm.

Area of trapezium= 1/2*8*(25+13)=152 cm^2

Answer 2

$\boxed {\text {Area of trapezium = }\dfrac{1}{2} ( a + b) ( h) }$

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Plug in the known values and find h:

$\dfrac{1}{2} (25 + 13) (h) = 57\sqrt{21}$

$19h = 57\sqrt{21}$

$h = 57\sqrt{21} \div 19$

$h = 3\sqrt{21}$

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Find the non-parallel side:

a² + b² = c²

(3√21)² + (25 - 13)² = c²

c² = 189 + 144

c = √333

c =3√37 cm

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Answer: The non-parallel side is 3√37 cm