Question

The area of a trapezium is 800 cm2

.Its parallel sides are 48 cm and 32 cm.
The distance between the parallel sides is

Answer 1

The distance between the parallel sides is 20cm.

Explanation:

Area of a trapezoid:

`A=(a+b)/(2)* h`

where a and b are the 2 bases, and h is the height. The value we're trying to find here is the height.

3 of the 4 variables in this equation are already given:

A = 800

a = 48

b = 32

Just plug those in and solve for h:

`\rightarrow 800=(48+32)/(2)* h\\\rightarrow 800=(80)/(2)* h\\\rightarrow 800=40* h\\\rightarrow 800/40=h\\\rightarrow h=20`

Answer 2

The distance between the parallel sides of trapezium is 20 cm.

Step-by-step explanation:

Here's the required formula to find the distance between the parallel sides of trapezium.

`\star\small{\underline{\boxed{\tt{\purple{A =(1)/(2) * \Big(Sum \: of \: parallel \: sides \Big)* h}}}}}`

• »» A = area
• »» h = height
• »» sum of parallel sides = a+b

Substituting all the given values in the formula to find the distance between the parallel sides of trapezium :

`{\implies{\sf{A = (1)/(2) * \Big(Sum \: of \: parallel \: sides \Big)* h}}}`

`{\implies{\sf{A = (1)/(2) * \Big( a + b\Big)* h}}}`

`{\implies{\sf{800 = (1)/(2) * \Big(48 + 32\Big)* h}}}`

`{\implies{\sf{800 = (1)/(2) * \Big( \: 80 \: \Big)* h}}}`

`{\implies{\sf{800 = (1)/(2) * 80 * h}}}`

`{\implies{\sf{800 = (80)/(2) * h}}}`

`{\implies{\sf{h = 800 * (2)/(80)}}}`

`{\implies{\sf{h = \cancel{800} * \frac{2}{\cancel{80}}}}}`

`{\implies{\sf{h = 10 * 2}}}`

`{\implies{\sf{h = 20 \: cm}}}`

`\star{\underline{\boxed{\sf{\red{Height = 20 \: cm}}}}}`

Hence, the height of trapezium is 20 cm.

`\rule{300}{2.5}`