area of shapes (trapezium)question edexcel

can someone pls help me with these questions
1.A trapezium of area 60cm^2 has parallel sides of length 12cm and 8cm.What is the distance between the two parallel sides?
2.A cylindrical water tank holds 26 litres when full.the water tank is 36cm tall.Work out the radius of the tank to 2d.p.

Reply 1

dcravenor

Area of a Trapezoid formula: A=((a+b)/2)*h

In other words 60 = ((12+8)/2)*h

Going to leave you the other one so you actually do something though 😂

Reply 2

_MB_

So for 1. You need to know the equation for the area of a trapezium, which is ((sum of the parallel sides/2)*distance between the sides))

Set your value of 60cm^2 equal to this equation. Let x be the distance between the sides and rearrange for X.

For 2, you would need to know that 26 litres is equivalent of 26000cm^3.

The volume of a cylinder is pi*r^2*height.Set that equal to 26000 and rearrange for r as you know the height.

Reply 3

WannabeLawyer01

Original post by error405

For question one you need to work backwards as the distance between the two parallel sides is just the height:
1/2 x (a+b) x h = the area of a trapezium
so knowing this, you wanna input the numbers you do have:
1/2 x (12+8) x h = 60
you can now solve for h:
1/2 x 20 x h = 60
10 x h = 60
h = 60/10 = 6cm

For question two, you need to know how to convert from liters to centimeters and how to find the volume of a prism:
1 litre = 1000 cubic centimeters
26 litres = 26000 cubic centimeters
Pi x r^2 x height = volume of the cylinder
Now input the numbers you have into the formula:
Pi x r^2 x 36 = 26000
First divide 26000 by (Pi x 36):
r^2 = 229.8904734
Now square root both sides:
r = 15.16213947
Finally round to an appropriate degree of accuracy. :smile: