Question

1. Find the area, in square metres, of the trape- zium whose bases and altitudes are given below:

(i) parallel sides 10 dm and 15 dm,
altitude = 8 dm.

(ii) parallel sides 250 cm and 50 dm,
altitude = 5 cm.​

Answer 1

Answer :-

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Concept\;:-}}}$

Here the concept of Areas of Trapezium has been used. We are given the parallel sides and the perpendicular height between them. First we will check that if these sides are in same unit. If they are, we will directly apply them in formula of Area of Trapezium. And if they aren't in same units, we will change them in same units and find the answer.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;(Sum\;of\;Parallel\;Sides)\;\times\;Height}}}$

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★ Solution :-

i.) For the First Case of Trapezium :-

Given,

» First among the Parallel sides = 10 dm

» Second among the Parallel sides = 15 dm

» Altitude = Height = 8 dm

This altitude is only the perpendicular distance between the parallel sides of Trapezium.

Since, here all the units are same, we can directly apply them in formula and find the answer.

$\\\;\;\;\sf{:\Longrightarrow\;\;Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;(Sum\;of\;Parallel\;Sides)\;\times\;Height}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;(10\;+\;15)\;\times\;8}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;25\;\times\;8}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;Area\;of\;Trapezium\;=\;\bf{25\;\times\;4}}$

$\\\;\;\;\bf{:\Longrightarrow\;\;Area\;of\;Trapezium\;=\;\bf{100\;\;dm^{2}}}$

We know that,

1 dm² = 0.01 m²

=> 100 dm² = 0.01 × 100 m²

=> 100 dm² = 1 m²

$\\\;\underline{\boxed{\tt{Area\;\;of\;\;Trapezium\;=\;\bf{1\;\;m^{2}}}}}$

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ii.) For the Second Case of Trapezium :-

Given,

» First among the Parallel Sides = 250 cm

» Second among the Parallel Sides = 50 dm

» Altitude = Height = 5 cm

This altitude is only the height of Trapezium commonly known as perpendicular distance between the parallel sides.

We know the relation that,

$\\\;\sf{:\mapsto\;\;1\;dm\;=\;\bf{10\;\;cm}}$

where,

dm = Decimetre

cm = Centimetre

$\\\;\sf{:\mapsto\;\;50\;dm\;=\;\bf{50\;\times\;10\;\;cm}}$

$\\\;\bf{:\mapsto\;\;50\;dm\;=\;\bf{500\;\;cm}}$

Since, all the units are same now. Then by applying these values, in the formula of Area of Trapezium, we get,

$\\\;\;\;\sf{:\Longrightarrow\;\;Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;(Sum\;of\;Parallel\;Sides)\;\times\;Height}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;(250\;+\;500)\;\times\;5}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;750\;\times\;5}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;3750}}$

$\\\;\;\;\bf{:\Longrightarrow\;\;Area\;of\;Trapezium\;=\;\bf{1875\;\;cm^{2}}}$

We know that,

1 cm² = 0.0001 m²

=> 1875 cm² = 1875 × 0.0001 m²

=> 1875 cm² = 0.1875 m²

$\\\;\underline{\boxed{\tt{Area\;\;of\;\;Trapezium\;=\;\bf{0.1875\;\;m^{2}}}}}$

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★ More to know :-

$\\\;\sf{Area\;of\;Rectangle\;=\;Length\;\times\;Breadth}$

$\\\;\sf{Area\;of\;Square\;=\;(Side)^{2}}$

$\\\;\sf{Area\;of\;Triangle\;=\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

$\\\;\sf{Area\;of\;Parallelogram\;=\;Base\;\times\;Height}$

$\\\;\sf{Area\;of\;Circle\;=\;\pi r^{2}}$

$\\\;\sf{Perimeter\;of\;Rectangle\;=\;2\;\times\;(Length\;+\;Breadth)}$

$\\\;\sf{Perimeter\;of\;Rectangle\;=\;4\;\times\;(Side)}$

$\\\;\sf{Perimeter\;of\;Circle\;=\;2\pi r}$

Answer 2

Answer:

:⟹AreaofTrapezium=100dm

2

We know that,

1 dm² = 0.01 m²

=> 100 dm² = 0.01 × 100 m²

=> 100 dm² = 1 m²

ii.) For the Second Case of Trapezium :-

Given,

» First among the Parallel Sides = 250 cm

» Second among the Parallel Sides = 50 dm

» Altitude = Height = 5 cm

This altitude is only the height of Trapezium commonly known as perpendicular distance between the parallel sides.

We know the relation that,

\begin{gathered}\\\;\sf{:\mapsto\;\;1\;dm\;=\;\bf{10\;\;cm}}\end{gathered}

:↦1dm=10cm

where,

dm = Decimetre

cm = Centimetre

$</p><p>\begin{gathered}\\\;\sf{:\mapsto\;\;50\;dm\;=\;\bf{50\;\times\;10\;\;cm}}\end{gathered} </p><p>:↦50dm=50×10cm</p><p> </p><p> </p><p></p><p>\begin{gathered}\\\;\bf{:\mapsto\;\;50\;dm\;=\;\bf{500\;\;cm}}\end{gathered} </p><p>:↦50dm=500cm</p><p> </p><p>$

Since, all the units are same now. Then by applying these values, in the formula of Area of Trapezium, we get,

We know that,

1 cm² = 0.0001 m²

=> 1875 cm² = 1875 × 0.0001 m²

=> 1875 cm² = 0.1875 m²