Question

One of the parallel sides of a trapezium is 6 cm longer than the other. If the height of the trapezium is 7cm and its area is 105 cm^2, find the length of the parallel sides. step by step explanation please ​

Answer 1

Given :-

• Area of the trapezium = 105 cm²
• Height of the trapezium = 7 cm
• One of the parallel sides is 6 cm more than other parallel side

$\sf ✯ \green {\: Formula \: of \: area \: of \: trapezium = \: \frac{1}{2} \times h \times (a + b)}$

• Let the length of side AB be x
• Therefore, length of side CD will be ( x + 6) cm

Now, putting the values in the formula of area of trapezium, we get :-

$\sf \longrightarrow { \frac{1}{2} \times 7 \times (x + x + 6) {cm}^{2} = 105 \: {cm}^{2} } \\ \sf \longrightarrow { \frac{7}{2} \times (2x + 6) \: {cm}^{2} \: = 105 \: {cm}^{2} } \: \: \: \: \: \: \: \: \: \: \: \\ \sf \longrightarrow {7 \times (2x + 6) {cm}^{2} = 105 {cm}^{2} \times 2} \: \: \: \: \: \: \: \\ \sf \longrightarrow {(14x + 42) {cm}^{2} = 210 \: {cm}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \longrightarrow {14x = (210 - 42) {cm}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \longrightarrow {x = \frac{ \cancel{168}}{ \cancel{14}} = 12 \: cm} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \longrightarrow \red {x = 12 \: cm} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf \blue{Since \: , \: x = 12 \: cm} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \pink{\therefore \: x + 6 = 12 + 6 = 18 \: cm}$

$\sf \therefore side \: AB = x = 12 cm \\ \sf and \: side \: CD \: = 18 \: cm$

$\sf\underline { More \: to \: know }:-$

• What is a trapezium?
• A closed polygon with a pair of parallel sides, is known as a trapezium.
• What is a closed polygon?
• A closed figure, made up of three or more than 3 lines is known as closed polygon

$\sf ✯ \gray {\: Formula \: of \: area \: of \: trapezium = \: \frac{1}{2} \times h \times (a + b)}$

Where,

• H = height
• a = first parallel side
• b = second parallel side

Note :- Please slide to see full solution.

Answer 2

Step-by-step explanation:

Given :-

Area of the trapezium = 105 cm²

Height of the trapezium = 7 cm

One of the parallel sides is 6 cm more than other parallel side

\sf ✯ \green {\: Formula \: of \: area \: of \: trapezium = \: \frac{1}{2} \times h \times (a + b)}✯Formulaofareaoftrapezium=

2

1

×h×(a+b)

Let the length of side AB be x

Therefore, length of side CD will be ( x + 6) cm

Now, putting the values in the formula of area of trapezium, we get :-

\begin{gathered} \sf \longrightarrow { \frac{1}{2} \times 7 \times (x + x + 6) {cm}^{2} = 105 \: {cm}^{2} } \\ \sf \longrightarrow { \frac{7}{2} \times (2x + 6) \: {cm}^{2} \: = 105 \: {cm}^{2} } \: \: \: \: \: \: \: \: \: \: \: \\ \sf \longrightarrow {7 \times (2x + 6) {cm}^{2} = 105 {cm}^{2} \times 2} \: \: \: \: \: \: \: \\ \sf \longrightarrow {(14x + 42) {cm}^{2} = 210 \: {cm}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \longrightarrow {14x = (210 - 42) {cm}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \longrightarrow {x = \frac{ \cancel{168}}{ \cancel{14}} = 12 \: cm} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \longrightarrow \red {x = 12 \: cm} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}

⟶

2

1

×7×(x+x+6)cm

2

=105cm

2

⟶

2

7

×(2x+6)cm

2

=105cm

2

⟶7×(2x+6)cm

2

=105cm

2

×2

⟶(14x+42)cm

2

=210cm

2

⟶14x=(210−42)cm

2

⟶x=

14

168

=12cm

⟶x=12cm

\begin{gathered}\sf \blue{Since \: , \: x = 12 \: cm} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \pink{\therefore \: x + 6 = 12 + 6 = 18 \: cm}\end{gathered}

Since,x=12cm

∴x+6=12+6=18cm

\begin{gathered}\sf \therefore side \: AB = x = 12 cm \\ \sf and \: side \: CD \: = 18 \: cm\end{gathered}

∴sideAB=x=12cm

andsideCD=18cm

\sf\underline { More \: to \: know }:-

Moretoknow

:−

What is a trapezium?

A closed polygon with a pair of parallel sides, is known as a trapezium.

What is a closed polygon?

A closed figure, made up of three or more than 3 lines is known as closed polygon

\sf ✯ \gray {\: Formula \: of \: area \: of \: trapezium = \: \frac{1}{2} \times h \times (a + b)}✯Formulaofareaoftrapezium=

2

1

×h×(a+b)

Where,

H = height

a = first parallel side

b = second parallel side

Note :- Please slide to see full solution

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