Question

In the trapezium ABCD, AB parallel
CD. Given AB = 24 cm and the distance between AB and CD is 10
cm. If the area of the trapezium ABCD is 210 cm2, find the length of CD.​

Answer 1

Answer:

Length of CD is 18 cm.

Step-by-step explanation:

Given :-

• In the trapezium ABCD, AB || CD.
• AB = 24 cm and the distance between AB and CD is 10 cm.
• Area of the trapezium ABCD is 210 cm².

To find :-

• Length of CD.

Solution :-

ABCD is a trapezium.

AB || CD

AB = 24 cm

Distance between AB and CD = Height of the trapezium

Then,

• Height of the trapezium = 10 cm.

★ Area of the trapezium is 210 cm².

• Formula used :

${\boxed{\sf{Area\:of\: trapezium=\dfrac{1}{2}\times(sum\:of\: parallel\: sides)\times\: height}}}$

According to the question,

$\mapsto \sf \: \dfrac{1}{2} \times (AB + CD) \times 10 = 210 \\ \\ \mapsto \sf \: 5(24 + CD) = 210 \\ \\ \mapsto \sf \: (24 + CD) = \dfrac{210}{5} \\ \\ \mapsto \sf \: 24 + CD= 42 \\ \\ \mapsto \sf \: CD\: = 42 - 24 \\ \\ \mapsto \sf \: CD= 18$

Therefore, the length of CD is 18 cm.

Answer 2

Step-by-step explanation:

Given that, in the trapezium ABCD, AB parallel CD. Given AB = 24 cm and the distance between AB and CD is 10 cm. If the area of the trapezium ABCD is 210 cm².

We have to find the length of CD.

Area of trapezium = 1/2 × (Sum of parallel side) × (Distance between them i.e. height)

Substitute the values,

→ 1/2 × (AB + CD) × 10 = 210

→ 1/2 × 10 (24 + CD) = 210

→ 5(24 + CD) = 210

→ 24 + CD = 210/5

→ 24 + CD = 42

→ CD = 42 - 24

→ CD = 18

Hence, the length of the CD is 18 cm.