Question

the area of a Trapezium is 850 square CM one of the parallel sides is 64 cm and the perpendicular distance between the parallel sides is 17 cm find the length of the Other parallel side

Answer 1

$\text{area of trapezium = } \frac{1}{2} (b_1 + b_2)h$

where b1 and b2 are the lengths of parallel sides and h is the perpendicular distance between them.

Given that Area = 850 cm^2
b1 = 64 cm
h = 17 cm
b2 = ?

$850 = \frac{1}{2} \times (64 + b_2) \times 17 \\ \\ \Rightarrow 64 + b_2 = \frac{850 \times 2}{17}$

$\Rightarrow 64 + b_2 = 50 \times 2 = 100 \\ \\ \Rightarrow b_2 = 100 - 64 \\ \\ \Rightarrow b_2 = 36 \: cm$

Other parallel side is 36cm long.

Answer 2

Area of trapezium= 1/2 × sum of parallel sides × perpendicular distance between the parallel sides  850cm = 1/2 × (64+x) × 17 => 50= 32 + x/2 => 18 = x/2 => x = 18 × 2 = 36cm  Hence, length of other parallel side is 36cm.