Question

The area of a trapezium is 360 sq cm and its altitude is 18cm. If one of the parallel sides is 12cm, find the other.​

Answer 1

Answer:

Hence, the value of x is 18 cm. Hence, the two parallel sides are 18 cm and 22 cm.

Step-by-step explanation:

The Area of the Trapezium.

Given :–

Area of the Trapezium = 360 cm²

Height of the Trapezium = 18 cm

We know :–

⠀⠀⠀⠀⠀⠀Formula for

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Area of a Trapezium :

\boxed{\bf{A = \dfrac{1}{2} \times (a + b) \times h}}

A=

2

1

×(a+b)×h

Where :-

A = Area of the Trapezium.

a = Parallel side of the Trapezium.

b = Parallel side of the Trapezium.

h = Height of the Trapezium.

Concept :-

Let the first parallel side be x .

According to the Question , the other parallel side is 4 cm more than the first parallel side.i.e,

The other parallel side is (x + 4).

Now , by putting this value in the formula for area of a Trapezium , we can find the required value.

Solution :-

Given :-

a = x cm

b = (x + 4) cm

A = 360 cm²

h = 18 cm

By using the formula and substituting the values in it, we get :-

\begin{gathered}:\implies \bf{A = \dfrac{1}{2} \times (a + b) \times h} \\ \\ \\ :\implies \bf{360 = \dfrac{1}{2} \times (x + x + 4) \times 18} \\ \\ \\ :\implies \bf{360 = \dfrac{1}{2} \times (2x + 4) \times 18} \\ \\ \\ :\implies \bf{360 = \dfrac{1}{2} \times 2(x + 2) \times 18} \\ \\ \\ :\implies \bf{360 = \dfrac{1}{\not{2}} \times \not{2}(x + 2) \times 18} \\ \\ \\ :\implies \bf{360 = (x + 2) \times 18} \\ \\ \\ :\implies \bf{360 = 18x + 36} \\ \\ \\ :\implies \bf{360 - 36 = 18x} \\ \\ \\ :\implies \bf{324 = 18x} \\ \\ \\ :\implies \bf{\dfrac{324}{18} = x} \\ \\ \\ :\implies \bf{18 = x} \\ \\ \\ \therefore \purple{\bf{x = 18 cm}}\end{gathered}

:⟹A=

2

1

×(a+b)×h

:⟹360=

2

1

×(x+x+4)×18

:⟹360=

2

1

×(2x+4)×18

:⟹360=

2

1

×2(x+2)×18

:⟹360=



2

1

×



2(x+2)×18

:⟹360=(x+2)×18

:⟹360=18x+36

:⟹360−36=18x

:⟹324=18x

:⟹

18

324

=x

:⟹18=x

∴x=18cm

Hence, the value of x is 18 cm.

⠀⠀⠀⠀⠀⠀First parallel side :-

⠀⠀⠀⠀⠀⠀⠀⠀⠀a = x = 18 cm

⠀⠀⠀⠀⠀⠀⠀⠀→⠀b = (x + 4)

⠀⠀⠀⠀⠀⠀⠀⠀⠀=> (18 + 4) cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀=> 22 cm

Hence, the two parallel sides are 18 cm and 22 cm.

Answer 2

Step-by-step explanation:

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