Question

The area of a trapezium is 800 cm2

Answer 1

Answer:

The distance between the parallel sides is 20cm.

Step-by-step explanation:

Area of a trapezoid:

$A=\frac{a+b}{2}\times h$

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:

$\rightarrow 800=\frac{48+32}{2}\times h\\\rightarrow 800=\frac{80}{2}\times h\\\rightarrow 800=40\times h\\\rightarrow 800\div40=h\\\rightarrow h=20$

Answer 2

Answer:

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.

$\star\small{\underline{\boxed{\tt{\purple{A =\dfrac{1}{2} \times \Big(Sum \: of \: parallel \: sides \Big)\times h}}}}}$

• »» 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 :

${\implies{\sf{A = \dfrac{1}{2} \times \Big(Sum \: of \: parallel \: sides \Big)\times h}}}$

${\implies{\sf{A = \dfrac{1}{2} \times \Big( a + b\Big)\times h}}}$

${\implies{\sf{800 = \dfrac{1}{2} \times \Big(48 + 32\Big)\times h}}}$

${\implies{\sf{800 = \dfrac{1}{2} \times \Big( \: 80 \: \Big)\times h}}}$

${\implies{\sf{800 = \dfrac{1}{2} \times 80 \times h}}}$

${\implies{\sf{800 = \dfrac{80}{2} \times h}}}$

${\implies{\sf{h = 800 \times \dfrac{2}{80}}}}$

${\implies{\sf{h = \cancel{800} \times \dfrac{2}{\cancel{80}}}}}$

${\implies{\sf{h = 10 \times 2}}}$

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

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

Hence, the height of trapezium is 20 cm.

$\rule{300}{2.5}$