Answer:
The distance between the parallel sides is 20cm.
Step-by-step explanation:
Area of a trapezoid:
[tex]A=\frac{a+b}{2}\times h[/tex]
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:
[tex]\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[/tex]
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.
[tex]\star\small{\underline{\boxed{\tt{\purple{A =\dfrac{1}{2} \times \Big(Sum \: of \: parallel \: sides \Big)\times h}}}}}[/tex]
Substituting all the given values in the formula to find the distance between the parallel sides of trapezium :
[tex]{\implies{\sf{A = \dfrac{1}{2} \times \Big(Sum \: of \: parallel \: sides \Big)\times h}}}[/tex]
[tex]{\implies{\sf{A = \dfrac{1}{2} \times \Big( a + b\Big)\times h}}}[/tex]
[tex]{\implies{\sf{800 = \dfrac{1}{2} \times \Big(48 + 32\Big)\times h}}}[/tex]
[tex]{\implies{\sf{800 = \dfrac{1}{2} \times \Big( \: 80 \: \Big)\times h}}}[/tex]
[tex]{\implies{\sf{800 = \dfrac{1}{2} \times 80 \times h}}}[/tex]
[tex]{\implies{\sf{800 = \dfrac{80}{2} \times h}}}[/tex]
[tex]{\implies{\sf{h = 800 \times \dfrac{2}{80}}}}[/tex]
[tex]{\implies{\sf{h = \cancel{800} \times \dfrac{2}{\cancel{80}}}}}[/tex]
[tex]{\implies{\sf{h = 10 \times 2}}}[/tex]
[tex]{\implies{\sf{h = 20 \: cm}}}[/tex]
[tex]\star{\underline{\boxed{\sf{\red{Height = 20 \: cm}}}}}[/tex]
Hence, the height of trapezium is 20 cm.
[tex]\rule{300}{2.5}[/tex]
