The area of a trapezium is 34 cm2
and its height is 4cm. One of the parallel sides of the trapezium
is 10 cm, find the other parallel side
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The area of a trapezium is 34 cm2
and its height is 4cm. One of the parallel sides of the trapezium
is 10 cm, find the other parallel side
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Verified answer
7 cm
Step-by-step explanation:
=> Area of trapeium = 34cm²
=> Length of parallel side=10 cm
=> Height=4cm
=> Let the length of other side be "x" cm
=> Area = ½ (sum of parallel sides) x (distance between them)
=> 34 = ½ (10 + x) (4)
=> 34 = ½ x (40 + 4x)
=> 34 = 20 + 2x
=> 2x = 34 - 20
=> 2x = 14
=> x = 14/2
=> x = 7 cm
Formula :-
[tex] \sf \: area \: of \: trapezium \: = \frac{1}{2} (a + b) \times h \\ \\ [/tex]
Given :-
To find :-
Solution :-
let the length of the other parallel side be = Bcm
now, by using formula of area of trapezium
[tex]:\implies\sf \: area \: of \: trapezim = \frac{1}{2} (a + b)h \\ \\ \\ :\implies\sf \: 34 = \frac{1}{2} (10 + b) \times 4 \\ \\ \\ :\implies\sf \: 34(10 + b) \times 2 \\ \\ \\ :\implies\sf \: 34 = 20 + 2b \\ \\ \\ [/tex]
[tex]:\implies\sf \: 34 - 20 = 2b \\ \\ \\:\implies\sf \: 14 = 2b \\ \\ \\ :\implies\sf \: \cancel \frac{14}{2} = b \\ \\ \\ :\implies\sf \: 7 = b \\ \\ \\ :\implies\sf \: b = 7 \\ \\ [/tex]
∴ length of the other parallel side is 7cm.
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