Question

EXERCISE 15.2
1. Tick(V) the correct answer.
(a) The length of the parallel sides of a trapezium is 30 cm, and 50 cm and its area is 800
What is the distance between the parallel sides?
(i) 10 cm (ii) 15 cm (iii) 20 cm (iv) 25 cm
​

Answer 1

✬ The distance between the parallel sides is 20 cm. option(iii)✬

Step-by-step explanation:

Given: The length of parallel sides of a trapezium are 30 cm and 50 cm and the area of trapezium is 800 cm².

To find: Distance between the parallel sides

Required Formula:

• Area of trapezium = ½ × h(a + b)

Where,

• A = Area of trapezium
• a = length of parallel side 1
• b = length of parallel side 2
• x = distance between the parallel sides(h)

Then,

$\\ :\implies\sf{800 = \frac{1}{2} \times x(30 + 50)} \\ \\ :\implies\sf{800 \times 2 = x(80)} \\ \\ :\implies\sf{1600 = 80x} \\ \\ :\implies\sf{x = \frac{1600}{80} } \\ \\ :\implies \underline{ \boxed{\frak{x = 20 \: cm}}} \: \red{ \bigstar}$

• Hence, The distance between the parallel sides is 20 cm.

Answer 2

Given: 

• Length of parallel sides of a trapezium are 30 cm and 50 cm 
• The area of trapezium is 800 cm².

To find: 

• Distance between the parallel sides

Required Formula:

$\: \: \: \boxed{\sf{Area \: of \: trapezium = \frac{1}{2} × h(a + b)}} \orange\bigstar$

Where,

• A = Area of trapezium
• a = length of parallel side 1
• b = length of parallel side 2
• x = distance between the parallel sides(h)

Then,

$\begin{gathered}\\ \implies\sf{800 = \frac{1}{2} \times x(30 + 50)} \\ \\ \implies\sf{800 \times 2 = x(80)} \\ \\ \implies\sf{1600 = 80x} \\ \\ \implies\sf {x = \cancel\frac{1600}{80} } \\ \\ :\implies \underline{ \boxed{\frak{x = 20 \: cm}}} \: \green{ \bigstar}\end{gathered}$

• Hence, The distance between the parallel sides is 20 cm.

Thank you!

@itzshivani