Question

Two parallel sides of a trapezium are of lengths 16 cm and 10 cm and the distance between them is 8 cm.Then area of trapezium is:
(explain in detail )​

Answer 1

Given -

• The length of parallel sides of parallelogram = 16cm and 10cm

• Distance between them = 8cm

To find -

• The area of parallelogram.

Formula used -

• Area of parallelogram = $\sf\frac{1}{2}$ × (sum of parallel sides) × Distance between them.

Solution -

In the question, we are provided with the length(s) of two parallel sides of a parallelogram, and the distance between them is 8cm, and we need to find the area of that parallelogram, for that we will use the formula of area of parallelogram, from that we will obtain our area. Let's do it!

According to Question -

Length of 1st side (a) = 16cm

Length of 2nd side (b) = 10cm

Distance between them (d) = 8cm

On Substituting The Values -

$\longrightarrow$ Area = $\sf\dfrac{1}{2}$ × (a + b) × (d)

$\longrightarrow$ Area = $\sf\dfrac{1}{2}$ × (16cm + 10cm) × 8cm

$\longrightarrow$ Area = $\sf\dfrac{1}{2}$ × 26cm × 8cm

$\longrightarrow$ Area = 26cm × 4cm

$\longrightarrow$ Area = 104cm²

$\therefore$ The area of the given parallelogram is 104cm²

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Answer 2

Given :-

• Two parallel sides of a trapezium are of length 16 cm and 10 cm and the distance between them is 8 cm.

To Find :-

• What is the area of the trapezium.

Formula Used :-

${\red{\boxed{\small{\bold{Area\: of\: trapezium =\: \dfrac{1}{2} \times (Sum\: of\: parallel\: sides) \times Distance\: between\: them}}}}}$

Solution :-

Given :

• Two parallel sides = 16 cm and 10 cm
• Distance between them = 8 cm

According to the question by using the formula we get,

$\\ \sf \implies Area\: of\: trapezium =\: \dfrac{1}{2} \times (16 + 10) \times 8$

$\\ \sf \implies Area\: of\: trapezium =\: \dfrac{1}{2} \times 26 \times 8$

$\\ \sf \implies Area\: of\: trapezium =\: \dfrac{1}{\cancel{2}} \times {\cancel{208}}$

$\\ \sf \implies \bold{\purple{Area\: of\: trapezium =\: 104\: {cm}^{2}}}$

${\underline{\boxed{\small{\bf{\therefore The\: area\: of\: trapezium\: is\: 104\: {cm}^{2}.}}}}}$

${\underline{\boxed{\large{\mathfrak{VERIFICATION :-}}}}}$

↦ $\sf Area\: of\: trapezium =\: \dfrac{1}{2} \times (16 + 10) \times 8$

By putting area of trapezium = 104 we get,

↦ $\sf 104 =\: \dfrac{1}{2} \times (16 + 10) \times 8$

↦ $\sf 104 =\: \dfrac{1}{\cancel2} \times {\cancel{208}}$

➠ 104 = 104

➦ LHS = RHS

Hence, Verified ✔