Question

the area of trapezium is 40cm^2.its parallel sides are 12cm and 8 cm find tge distance between parallel.sides is​

Answer 1

• Distance between parallel sides 12 cm and 8 cm is 4 cm.

Step-by-step explanation:

To find:-

• Distance between parallel sides.

Solution:-

Given that,

Area of trapezium is 40 cm².

Length of parallel sides are 12 cm and 8 cm.

Area of trapezium = (a + b)/2 × h

• Here, a and b are parallel sides .
• And h is distance between parallel sides.

So,

➝ 40 = (12 + 8)/2 × h

➝ 40 = 20/2 × h

➝ 40 × 2 = 20 × h

➝ 80 = 20 × h

➝ 80/20 = h

➝ 4 = h

Or, ➝ h = 4

Verification:-

➝ 40 = (12 + 8)/2 × h

• Put h = 4

➝ 40 = (12 + 8)/2 × 4

➝ 40 = 20/2 × 4

➝ 40 = 10 × 4

➝ 40 = 40

Hence, Verified!!.

h is distance between parallel sides which is 4 cm.

Therefore,

Distance between parallel sides 12 cm and 8 cm is 4 cm.

Answer 2

Step-by-step explanation:

Given :

• the area of trapezium is 40cm^2.

• its parallel sides are 12cm and 8 cm

To Find :

• the distance between parallel.sides is

Solution :

Concept :

• Trapezium is a type of quadrilateral in which two sides are parallel to each other there are many types of trapezium which are given in the above fig.

Here we will learn how to use the formula to find the area of trapezium.

• Area of trapezium ABCD = Area of ∆ ABD + Area of ∆ CBD

• = 1/2 × a × h + 1/2 × b × h

• = 1/2 × h × (a + b)

• = 1/2 (sum of parallel sides) × (perpendicular distance between them)

_______________________

$: \implies \: \: \: \: \: \boxed{ \sf \: area \: of \: trapezium \: = \frac{1}{2} \times h \times (a + b)}$

Substitute all values

$: \implies \sf \: \: \: \: \: \:40 = \frac{1}{2} \times h \times (12 + 8) \\ \\ \\ : \implies \sf \: \: \: \: \: \:40 = \frac{1}{2} \times h \times 20 \\ \\ \\ \: : \implies \sf \: \: \: \: \: \:40 = \frac{1}{2} \times 20h \\ \\ \\ : \implies \sf \: \: \: \: \: \:80 = 20h \\ \\ \\ : \implies \sf \: \: \: \: \: \:h = \cancel{\frac{80}{20} } \\ \\ \\ : \implies \sf \: \: \: \: \: \:h = 4$

• Hence the distance between parallel. sides is 4 cm