Question

The area of an isosceles trapezium is 80 sq cm.
If the parallel sides are 4 cm and 16 cm, find
the (i) height' (ii) length of non-parallel sides.​

Answer 1

Given :-

• Area of an isosceles trapezium = 890 cm².
• Parallel sides of the trapezium = 4 cm and 16 cm.

To Find :-

• The height and the length of non parallel sides.

Solution :-

Area of trapezium :-

$\boxed{\underline{\pink{\sf \dfrac{1}{2} \times height \times (Sum \:of\:all \:parallel\:sides)}}}$

$:\implies\:\sf{890 = \dfrac{1}{2} \times h \times (4 +16) }$

$:\implies\:\sf{890 \times 2 = h \times 20 }$

$:\implies\:\sf{1780 = h \times 20 }$

$:\implies\:\sf{h= \dfrac{1780}{20} }$

$:\implies\:\sf{h= 89\:cm^2}$

Length of non parallel side :-

$:\implies\sf{\sqrt{8^2 + 6^2} }$

$:\implies\sf{\sqrt{100} }$

$:\implies\sf{10\:cm}$

∴  Length of non paralle side =  10 cm