Answer

Verified

448.8k+ views

**Hint:**A trapezium is a quadrilateral which is defined as a shape with four sides and one set of parallels side.

The line segment connecting the midpoints of the non-parallel sides of a trapezoid is called the mid-segment.

If we drew a line segment, between the two non-parallels sides. From the mid-point of both sides, the trapezium will be divided into two unequal parts.

Area\[ = \dfrac{k}{2}(AB + CD)\]

We know that

Area of trapezoid \[ = \]area of triangle (1)\[ + \] area of rectangle \[ + \]area of triangle (2)

That means

\[A = \dfrac{{ah}}{2} + bh + \dfrac{{ch}}{2}\]

\[A = \dfrac{{ah + 2{b_1}h + cb}}{2}\]

Simplifying the equation, rearranging the term and factoring result to

\[A = \dfrac{h}{2}\left[ {{b_1}\_(a + {b_1}\_c)} \right].........(1)\]

We assume the longer base of the trapezium be \[{b_2}\] then

\[{b_2} = a + {b_1} + c...........(2)\]

Substituting (2) in equation (1)

\[A = \dfrac{h}{2}\left( {{b_1} + {b_2}} \right)\]

Therefore, the arc of trapezium with b bases \[{b_1} + {b_2}\] and altitude h is

\[A = \dfrac{h}{2}\left( {{b_1} + {b_2}} \right)\]

Therefore

**Complete step by step answer:**

Given image= where ADCE is a rectangle

Given

\[BE = 3cm\] \[AB = 3 + 3 = 6cm\]

\[EA = 3cm\] \[CD = 3cm\]

\[AD = 8cm\] \[AD = 8cm\]

Area of trapezium \[ABCD = \dfrac{1}{2} \times \] parallel sides \[ \times \]height

\[ = \dfrac{1}{2} \times (AB + CD) \times AD\]

\[ = \dfrac{1}{2} \times (6 + 3) \times 8\] {BY putting the value of AB, CD and Ad in the formula}

\[ = \dfrac{1}{2} \times 9 \times 8 = 36c{m^2}\]

Hence,

The area of the trapezium

\[ABCD = 36c{m^2}\]

**Note:**Properties of trapezium

The sum of all the four angles of the trapezium is equal to \[{360^0}\]

It has two parallels and two non-parallels sides

The diagonals of regular trapezium bisect each other

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

Two Paris of adjacent angles of trapezium formed between the parallel’s sides and one of the non-parallels side, add up to 180 degrees.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths