Question

If the parallel sides of a trapezium are 2 cm apart and their sum is 10 cm then its
area is:

Answer 1

A n s w e r

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G i v e n

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• Parallel sides of a trapezium are 2 cm apart

• Sum of parallel sides is 10 cm

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F i n d

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• Area of trapezium

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S o l u t i o n

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$\underline{\bold{\texttt{Area of trapezium :}}}$

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➠ $\sf \dfrac { 1 } { 2 } \times (l_{1} + l_{2}) \times h$ ⚊⚊⚊⚊ ⓵

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Where ,

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➻ $\sf l _{ 1 }$ = Length of 1st parallel side

➻ $\sf l_ { 2 }$ = Length of 2nd parallel side

➻$\sf h$ = Distance between the parallel sides

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$\underline{\bold{\texttt{Area of given trapezium :}}}$

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Given that , Parallel sides are 2 cm apart and Sum of parallel sides is 10 cm

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Thus ,

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• $\sf l _{ 1 } + l _{ 2 } = 10$

• $\sf h = 2$

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⟮ Putting the above values in ⓵ ⟯

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➜ $\sf \dfrac { 1 } { 2 } \times (l_{1} + l_{2}) \times h$

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➜ $\sf \dfrac { 1 } { 2 } \times (10) \times 2$

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➨ 10 sq. cm.

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• Hence the area of trapezium is 10 sq. cm.

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Additional information

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Perimeter of trapezium

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• a + b + c + d

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Where ,

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➻ a = Length of 1st side

➻ b = Length of 2nd side

➻ c = Length of 3rd side

➻ d = Length of 4th side

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Properties of trapezium

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• The sum of all the four angles of the trapezium is equal to 360°

• A trapezium has two parallel sides and two non-parallel sides

• The diagonals of regular trapezium bisect each other

• The length of the mid-segment is equal to half the sum of the parallel bases, in a trapezium

Answer 2

$\large{\underbrace{\sf{\orange{required \: solution:}}}}$

given that,

• The parallel sides of a trapezium are 2 cm apart.
• Their sum is 10 cm

☯️we need to find the area of the trapezium.

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according to the question,

$\bf {required \: formulae : }$

${: \implies \bf \underline \blue{ \frac{1}{2} \times sum \: of \: parallel \: sides \times h }}$

• sum of parallel sides = 10 (given)

• h = height = distance between them = 2cm

$: \implies \sf \frac{1}{2} \times (10) \times 2 \\ \\ : \implies \sf\:{5 \times 2} \\ \\ \: \: \: \: \: \: : \implies \bf \underline \green{\: {10cm}^{2} }$

hence , The area of the trapezium is 10cm²

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