Question

the area of trapezium is 210 sq cm its parallel sides are ratio 1:2 and distance between them is 14 cm find the length of each parallel sides​

Answer 1

Answer:

10cm & 20cm.

Explanation:

In a trapezium,

Ratio of parallel sides 1 : 2

Area is 210cm²

Distance between the parallel sides is 14cm.

We know that,

Area of a trapezium :

→ ½ • sum of parallel sides • distance between the parallel sides.

Let's say the parallel sides are ‘x’ and ‘2x’

According to the question :

→ 210 = ½ • (x + 2x) • 14

→ 210 = 3x • 7

→ 210 = 21x

→ 210/21 = x

→ 10 = x

Hence, the parallel sides measures :

→ ‘x’ and ‘2x’

Or, 10 and 2(10)

Or, 10cm and 20cm.

Required answer : 10cm & 20cm.

Answer 2

Answer:

$\LARGE\underline{\sf \pmb{Given}}$

• ➠ The area of trapezium is 210
• ➠The trapezium parallel sides are ratio 1:2
• ➠ Distance between them is 14 cm

$\begin{gathered} \end{gathered}$

$\LARGE \underline{\sf {\pmb{To \: Find }}}$

• ➠ The length of each parallel sides

$\begin{gathered} \end{gathered}$

$\LARGE\underline {\sf {\pmb{Using\: Formula }}}$

${\underline {\boxed {\bf{Area \: of \: Trapezium = \dfrac{1}{2} ( Sum \: of \: Parallel \: sides) \times Height}}}}$

$\begin{gathered} \end{gathered}$

$\LARGE \underline {\sf \pmb{Understanding \: The \: Question }}$

In this question the area of Trapezium is 210 cm² and its parallel sides are in ratio 1:2 and distance between them is 14 cm (we can also call it height of Trapezium).In this question we need to find the each parallel sides of Trapezium

$\begin{gathered}\end{gathered}$

$\LARGE{\underline{\sf \pmb{Solution}}}$

Let the measurement parallel sides of Trapezium be "x" and "2x"

So,

${ \red\implies \bf \green{Area \: of \: Trapezium = \dfrac{1}{2} ( Sum \: of \: Parallel \: sides) \times Height}}$

• ➥ Substituting the values

${ \implies \sf {200 \: {cm}^{2} = \dfrac{1}{2} ( x + 2x) \times14}}$

${ \implies \sf {210 = \dfrac{1}{\cancel{2} }\times 3x\times \cancel{14}}}$

${ \implies \sf {210 =3x \times 7}}$

${ \implies \sf {210 =21x}}$

$\implies \sf \cancel\dfrac{210}{21} = x$

$\implies \bf 10 \: cm = x$

Here

$\underline{\large {\boxed{ \bf\red{x = 10 \: cm}}}}$

$\begin{gathered} \end{gathered}$

$\LARGE\underline {\sf \pmb{Therefore}}$

Sides

• ➥ 10 = 10 cm
• ➥ 2 × 10 = 20 cm

$\begin{gathered}\end{gathered}$

$\LARGE\underline {\sf {\pmb{Verification}}}$

${ \red\implies \bf \green{Area \: of \: Trapezium = \dfrac{1}{2} ( Sum \: of \: Parallel \: sides) \times Height}}$

• ➥ Substituting the values

${ \implies \sf {200 \: {cm}^{2} = \dfrac{1}{2} ( 10 + 20) \: cm \times14 \: cm}}$

${ \implies \sf {210 \: {cm}^{2} = \dfrac{1}{\cancel{2} }\times 30 \: cm\times \cancel{14}}} \: \sf cm$

${ \implies \sf {210 \: {cm}^{2} =30 \: cm \times 7 \: cm}}$

${ \implies \bf {210 \: {cm}^{2} = 210 \: {cm}^{2} }}$

Here

$\underline {\boxed {\bf {\red{LHS = RHS}}}}$

• ➥ Hence Verified ✔

$\begin{gathered} \end{gathered}$

$\LARGE\underline {\sf \pmb{Additional \: Information }}$

$\begin{gathered}\begin{gathered}\bigstar \: \bf\underline{More \: Useful \: Formulae } \: \bigstar  \\ \begin{gathered}{\boxed{\begin{array} {cccc}{\sf{\leadsto{Perimeter \: of \: Trapezium = (Sum \: of \: all \: sides)}}} \\ \\ {\sf{{\leadsto TSA \: of \: cube \: = \: 6(side)^{2}}}} \\  \\{\sf{{\leadsto LSA \: of \: cube \:= \: 4(side)^{2}}}}  \\  \\{\sf{{\leadsto Volume \: of \: cube \: = \: (side)^{3}}}} \\  \\ {\sf{{\leadsto Diagonal \: of \: cube \: = \: \sqrt(l^{2} + b^{2} + h^{2}}}} \\  \\ {\sf{{\leadsto Perimeter \: of \: cube \: = \: 4(l+b+h)}}} \\  \\ {\sf{{\leadsto CSA \: of \: sphere \: = \: 2 \pi r^{2}}}} \\  \\ {\sf{{\leadsto SA \: of \: sphere \: = \: 4 \pi r^{2}}}} \\  \\{\sf{{\leadsto TSA \: of \: sphere \: = \: 3 \pi r^{2}}}} \\  \\ {\sf{{\leadsto Diameter \: of \: circle \: = \: 2r}}} \\  \\ {\sf{{\leadsto Radius \: of \: circle \: = \: \dfrac{d}{2}}}} \\  \\ {\sf{{\leadsto Volume \: of \: sphere \: = \: \dfrac{4}{3} \pi r^{3}}}} \\  \\ {\sf{{\leadsto Area \: of \: rectangle \: = \: Length \times Breadth}}} \\  \\ {\sf{{\leadsto Perimeter \: of \: rectangle \: = \:2(length+breadth)}}} \\  \\{\sf{{\leadsto Perimeter \: of \: square \: = \: 4 \times sides}}}\end{array}}}\end{gathered}\end{gathered}\end{gathered}$