Question

The area of a trapezium is 480 cm2, the distance between two parallel sides is 15 cm and one of the parallel side is 20 cm. The other parallel side is​

Answer 1

$\underline{\underline{\sf SOLUTION :}}$

To solve this type of questions first we have to write the all given parameters and then we have to write unknown values and then we have to proceed our answer. So,first we will write our given data :

• Area of trapezium = 480 cm²
• The distance between two parallel sides = 15 cm
• One parallel side is 20 cm.

Here we need to find the other parallel side. So, first assume the other parallel side as x. Then we have to just plug in the known values in given below formula :

• Area of trapezium = ½ × (Sum of parallel sides) × (distance between two parallel sides)

$\\\dag \: \underline{\underline{\textsf{According to the Question Now :}}}$

$:\implies\sf Area \: of \: trapezium = \dfrac{1}{2} \times (Sum \: of \: parallel \: sides) \times (Distance \: between\: the \: two \: parallel \: sides)$

$:\implies\sf 480 = \dfrac{1}{2} \times (20 + x) \times 15$

$:\implies\sf \dfrac{480}{15} = \dfrac{1}{2} \times (20 + x)$

$:\implies\sf 32 = \dfrac{1}{2} \times (20 + x)$

$:\implies\sf 32 \times 2= 20 + x$

$:\implies\sf 64= 20 + x$

$:\implies\sf x = 64 - 20$

$:\implies \underline{ \boxed{\sf x = 44 \: cm}}$

Answer 2

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➡️Here in this query , we have to find the length of the other parallel side of the trapezium. We will find the length of the other parallel side by using the area of the trapezium formula.

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➡️In the attachment .

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• Area of the trapezium ➡️ 480 cm²

• Height,h ➡️ 15 cm

• Length of one parallel side , a ➡️ 20 cm

$\bigstar { \underline {\bf{ \purple{ To} \: FinD}}} \bigstar$

• Length of the other parallel side , b ➡️ ?

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$\small\bigstar {\underline {\boxed { \bf {\green\:area \: of \: the \: trapezium \: = \frac{1}{2} (sum \: of \: the \: parallel \: sides) \times height}}}} \bigstar$

$\bigstar { \underline {\bf{ \purple{ SoLu}TioN}}} \bigstar$

Applying the formula of area of the trapezium ,

$\small \bf \implies{Area \: of \: the \: trapezium \: = \frac{1}{2} (sum \: of \: the \: parallel \: sides) \times height}$

$\small \bf \implies{Area \: of \: the \: trapezium \: = \frac{1}{2} (a + b) \times h}$

$\small \bf \implies{480 \: = \frac{1}{2} (20 + b) \times 15}$

$\small \bf \implies{ \frac{1}{2} (20 + b) \times 15=480}$

$\small \bf \implies{ \frac{1}{2} (20 + b) } = \cancel\frac{480}{15}$

$\small \bf \implies{ \frac{1}{2} (20 + b) =32}$

$\small \bf \implies{ 20 + b =32 \times 2}$

$\small \bf \implies{20 + b=64}$

$\small \bf \implies{b = 64 - 20}$

$\small \bf \implies{ \boxed{ \bf b=44 \: cm}}$

$\small \sf \therefore \: The \: length \: of \: the \: other \: parallel \: side,b \: is \: 44 \: cm$

$\bigstar { \underline {\bf{ \purple{ Expl}ore \: \pink{ Mo}re}}} \bigstar$

Formula:-

◼️Here is the formula of the area of the trapezium ➡️

$\small \purple\bigstar {\underline {\boxed { \bf {\green\:area of \: the \: trapezium \: = \frac{1}{2} (sum \: of \: the \: parallel \: sides) \times height }}}} \blue\bigstar \\ \small \bf or$

$\small\red \bigstar {\underline {\boxed { \bf {\green\:area of \: the \: trapezium \: = \frac{1}{2} (a + b) \times h }}}} \pink\bigstar$

Here ,

• 'a' and 'b' are the length of the parallel sides.

• 'h' is the perpendicular distance between 'a' and 'b' .

Area:-

• The surface covered by the border line of the figure is the area of the plain shape.

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